A rocket is intended to leave the Earth's garvitational field.The fuel in its main engine is a little less than the amount that is necessary and an auxliary engine, (only capable of operating for a short time) has to be used as well.When is it best to switch on the auxiliary engine?

Anoop Gaur started 'Cat's Eye', a company for providing cyber security solutions to businesses. Its objective to prevent, detect, respond to cyber attacks and protect critical data. He was a hardworking software engineer and an expert in cyber security. His reputation grew by leaps and bounds as he was not only a person of integrity but also did his work with almost honesty and sincerity. The business started growing day by day. He was delighted when he was offered a big project by the Ministry of Science and Technology. While working on the project he found that the volume of work made it impractical for him to handle all the work by himself. Therefore he decided to expand the team. The company maintained a close liaision with an engineering college in the State. During a campus placement, Aarav and Pranshi were appointed to work for the new project. He found the new employees capable, enthusiastic and trustworthy. Anoop Gaur was thus, able to focus on the objectives and with the help of Aarav and Pranshi, the object was completed on time. Not only this, Anoop Gaur was also able to extend his area of operations. On the other hand, Aarav and Pranshi also got opportunities to develop and exercise initiactive. (a) Identify and explain briefly the concept used by Anoop Gaur in the above case which helped him in focussing on the objectives. (b) Also, explain any four points of importance of the concept identified in part (a).

A satellite of mass m is going around the earth in a circular orbital at a height (R)/(2) from the surface of the earth. The satellite has lived its life and a rocket, on board, is fired to ake it leave the gravity of the earth. The rocket remains active for a very small interval of time and imparts an impulse in the direction of motion of the satellite. Neglect any hange in mass due to firing of the rocket. Find the minimum impulse imparted by the rocket to the satellite. Find the minimum work done by the rocket engine. Mass of the earth = M, Radius of the earth = R

A fuel cell is a cell that is continuously supplied with an oxidant and a reductant so that it can deliver a current indefinitely. Fuel cell offer the possibility of achieving high thermodynamic efficiency in the conversion of Gibbs energy into mechanical work. Internal combustion engines at best convert only the fraction (T_(2)-T_(1))T_(2) of heat of combustion into mechanical work. While the thermodynamic efficiency of the fuel cell is give by, eta=(|DeltaG|)/(|DeltaH|) , where DeltaG is the Gibbs energy change for the cell reaction and DeltaH is the enthalpy change of the cell reaction. This efficiency can be upto 80%-90% also in contrast to normal heat engine efficiency which are generally about 40% Fuel cells may be classified according to the temperature range in wich they operate low temperature (25 to 100^(@)C ), medium temperature (100 to 500^(@)C) ), high temperature (500 "to" 1000^(@)C) and very high temperature is that catalyst for the various steps in the process are not so necessary. Polarization of a fuel cell reduces the current. Polarization is the result of slow reactions or processes such as diffusion in the cell. The figure indicates the construction of hydrogen-oxygen fuel cell with a solid electrolyte, which is an ion exchange membrane. The membrane is impermeable to the reactant gases, but is permeable to hydrogen ions, which carry the current between the electrodes. To facillitate the operation finely divided platinum that function as a catalyst. Water is drained out of the cell during operation. Fuel cells of this general type have been used successfully in the space program and are quite efficient. their disadvantages for large-scale commercial application are that hydrogen presetns storage problems, and platinum is an expensive catalyst. Cheaper catalysts have been found for higher temperature operatureof hydrogen-oxygen fuel cells. Fuel cells taht use hydrocarbons and air have been developed, but their power per unit weight is too low to make them practical in ordinary automobiles. Better catalysts are needed. A hydrogen-oxygen fuel cell may hae an acidic or alkaline electrolyte. The half-cell reactions are: (1)/(2)O_(2)(g)+2H^(+)+2e^(-)rarrH_(2)O(l) E^(@)=1.2288V 2H^(+)+2e^(-)rarrH_(2)(g)E^(@)=0 H_(2)(g)+(1)/(2)O_(2)(g)rarrH_(2)O(l) E^(@)=1.2288V or (1)/(2)O_(2)(g)+H_(2)O(g)+2e^(-)rarr2OH^(-) E^(@)=0.4009V 2H_(2)O(l)+2e^(-)rarrH_(2)(g)+2OH^(-)E^(@)=-0.8279V H_(2)(g)+(1)/(2)O_(2)(g)rarrH_(2)O(l) E^(@)=1.2288V To maximize the power per unit mass of an electrochemical cell, the electronic and electrolytic resistances of the cell must be minimized. than aqueous solutions, high-temperature electrochemical cells are of special interest for practical applications. High temperature also allow the use of liquid metal electrode, which makes possibel high current densities than solid electrodes. If 567.5 mL of H_(2) gas at STP is fed into and is consumed by the cell in 10minutes, then what is the current output (in A) of the fuel cell?

A fuel cell is a cell that is continuously supplied with an oxidant and a reductant so that it can deliver a current indefinitely. Fuel cell offer the possibility of achieving high thermodynamic efficiency in the conversion of Gibbs energy into mechanical work. Internal combustion engines at best convert only the fraction (T_(2)-T_(1))T_(2) of heat of combustion into mechanical work. While the thermodynamic efficiency of the fuel cell is give by, eta=(|DeltaG|)/(|DeltaH|) , where DeltaG is the Gibbs energy change for the cell reaction and DeltaH is the enthalpy change of the cell reaction. This efficiency can be upto 80%-90% also in contrast to normal heat engine efficiency which are generally about 40% Fuel cells may be classified according to the temperature range in wich they operate low temperature (25 to 100^(@)C ), medium temperature (100 to 500^(@)C) ), high temperature (500 "to" 1000^(@)C) and very high temperature is that catalyst for the various steps in the process are not so necessary. Polarization of a fuel cell reduces the current. Polarization is the result of slow reactions or processes such as diffusion in the cell. The figure indicates the construction of hydrogen-oxygen fuel cell with a solid electrolyte, which is an ion exchange membrane. The membrane is impermeable to the reactant gases, but is permeable to hydrogen ions, which carry the current between the electrodes. To facillitate the operation finely divided platinum that function as a catalyst. Water is drained out of the cell during operation. Fuel cells of this general type have been used successfully in the space program and are quite efficient. their disadvantages for large-scale commercial application are that hydrogen presetns storage problems, and platinum is an expensive catalyst. Cheaper catalysts have been found for higher temperature operatureof hydrogen-oxygen fuel cells. Fuel cells taht use hydrocarbons and air have been developed, but their power per unit weight is too low to make them practical in ordinary automobiles. Better catalysts are needed. A hydrogen-oxygen fuel cell may hae an acidic or alkaline electrolyte. The half-cell reactions are: (1)/(2)O_(2)(g)+2H^(+)+2e^(-)rarrH_(2)O(l) E^(@)=1.2288V 2H^(+)+2e^(-)rarrH_(2)(g)E^(@)=0 H_(2)(g)+(1)/(2)O_(2)(g)rarrH_(2)O(l) E^(@)=1.2288V or (1)/(2)O_(2)(g)+H_(2)O(g)+2e^(-)rarr2OH^(-) E^(@)=0.4009V 2H_(2)O(l)+2e^(-)rarrH_(2)(g)+2OH^(-)E^(@)=-0.8279V H_(2)(g)+(1)/(2)O_(2)(g)rarrH_(2)O(l) E^(@)=1.2288V To maximize the power per unit mass of an electrochemical cell, the electronic and electrolytic resistances of the cell must be minimized. than aqueous solutions, high-temperature electrochemical cells are of special interest for practical applications. High temperature also allow the use of liquid metal electrode, which makes possibel high current densities than solid electrodes. What is the substance X taken out at bottom of the fuel cell shown in the figure?

A fuel cell is a cell that is continuously supplied with an oxidant and a reductant so that it can deliver a current indefinitely. Fuel cell offer the possibility of achieving high thermodynamic efficiency in the conversion of Gibbs energy into mechanical work. Internal combustion engines at best convert only the fraction (T_(2)-T_(1))T_(2) of heat of combustion into mechanical work. While the thermodynamic efficiency of the fuel cell is give by, eta=(|DeltaG|)/(|DeltaH|) , where DeltaG is the Gibbs energy change for the cell reaction and DeltaH is the enthalpy change of the cell reaction. This efficiency can be upto 80%-90% also in contrast to normal heat engine efficiency which are generally about 40% Fuel cells may be classified according to the temperature range in wich they operate low temperature (25 to 100^(@)C ), medium temperature (100 to 500^(@)C) ), high temperature (500 "to" 1000^(@)C) and very high temperature is that catalyst for the various steps in the process are not so necessary. Polarization of a fuel cell reduces the current. Polarization is the result of slow reactions or processes such as diffusion in the cell. The figure indicates the construction of hydrogen-oxygen fuel cell with a solid electrolyte, which is an ion exchange membrane. The membrane is impermeable to the reactant gases, but is permeable to hydrogen ions, which carry the current between the electrodes. To facillitate the operation finely divided platinum that function as a catalyst. Water is drained out of the cell during operation. Fuel cells of this general type have been used successfully in the space program and are quite efficient. their disadvantages for large-scale commercial application are that hydrogen presetns storage problems, and platinum is an expensive catalyst. Cheaper catalysts have been found for higher temperature operatureof hydrogen-oxygen fuel cells. Fuel cells taht use hydrocarbons and air have been developed, but their power per unit weight is too low to make them practical in ordinary automobiles. Better catalysts are needed. A hydrogen-oxygen fuel cell may hae an acidic or alkaline electrolyte. The half-cell reactions are: (1)/(2)O_(2)(g)+2H^(+)+2e^(-)rarrH_(2)O(l) E^(@)=1.2288V 2H^(+)+2e^(-)rarrH_(2)(g)E^(@)=0 H_(2)(g)+(1)/(2)O_(2)(g)rarrH_(2)O(l) E^(@)=1.2288V or (1)/(2)O_(2)(g)+H_(2)O(g)+2e^(-)rarr2OH^(-) E^(@)=0.4009V 2H_(2)O(l)+2e^(-)rarrH_(2)(g)+2OH^(-)E^(@)=-0.8279V H_(2)(g)+(1)/(2)O_(2)(g)rarrH_(2)O(l) E^(@)=1.2288V To maximize the power per unit mass of an electrochemical cell, the electronic and electrolytic resistances of the cell must be minimized. than aqueous solutions, high-temperature electrochemical cells are of special interest for practical applications. High temperature also allow the use of liquid metal electrode, which makes possibel high current densities than solid electrodes. For a hydrogen-oxygen fuel cell if DeltaH_(f)^(2)(H_(2)O,l)=-285kJ//""mole"" , then what will be its thermodynamic efficiency under standard conditions (use data given in the passage if required)?

A fuel cell is a cell that is continuously supplied with an oxidant and a reductant so that it can deliver a current indefinitely. Fuel cell offer the possibility of achieving high thermodynamic efficiency in the conversion of Gibbs energy into mechanical work. Internal combustion engines at best convert only the fraction (T_(2)-T_(1))T_(2) of heat of combustion into mechanical work. While the thermodynamic efficiency of the fuel cell is give by, eta=(|DeltaG|)/(|DeltaH|) , where DeltaG is the Gibbs energy change for the cell reaction and DeltaH is the enthalpy change of the cell reaction. This efficiency can be upto 80%-90% also in contrast to normal heat engine efficiency which are generally about 40% Fuel cells may be classified according to the temperature range in wich they operate low temperature (25 to 100^(@)C ), medium temperature (100 to 500^(@)C) ), high temperature (500 "to" 1000^(@)C) and very high temperature is that catalyst for the various steps in the process are not so necessary. Polarization of a fuel cell reduces the current. Polarization is the result of slow reactions or processes such as diffusion in the cell. The figure indicates the construction of hydrogen-oxygen fuel cell with a solid electrolyte, which is an ion exchange membrane. The membrane is impermeable to the reactant gases, but is permeable to hydrogen ions, which carry the current between the electrodes. To facillitate the operation finely divided platinum that function as a catalyst. Water is drained out of the cell during operation. Fuel cells of this general type have been used successfully in the space program and are quite efficient. their disadvantages for large-scale commercial application are that hydrogen presetns storage problems, and platinum is an expensive catalyst. Cheaper catalysts have been found for higher temperature operatureof hydrogen-oxygen fuel cells. Fuel cells taht use hydrocarbons and air have been developed, but their power per unit weight is too low to make them practical in ordinary automobiles. Better catalysts are needed. A hydrogen-oxygen fuel cell may hae an acidic or alkaline electrolyte. The half-cell reactions are: (1)/(2)O_(2)(g)+2H^(+)+2e^(-)rarrH_(2)O(l) E^(@)=1.2288V 2H^(+)+2e^(-)rarrH_(2)(g)E^(@)=0 H_(2)(g)+(1)/(2)O_(2)(g)rarrH_(2)O(l) E^(@)=1.2288V or (1)/(2)O_(2)(g)+H_(2)O(g)+2e^(-)rarr2OH^(-) E^(@)=0.4009V 2H_(2)O(l)+2e^(-)rarrH_(2)(g)+2OH^(-)E^(@)=-0.8279V H_(2)(g)+(1)/(2)O_(2)(g)rarrH_(2)O(l) E^(@)=1.2288V To maximize the power per unit mass of an electrochemical cell, the electronic and electrolytic resistances of the cell must be minimized. than aqueous solutions, high-temperature electrochemical cells are of special interest for practical applications. High temperature also allow the use of liquid metal electrode, which makes possibel high current densities than solid electrodes. The advantage of using fuel cell in a motorcar could be:

A fuel cell is a cell that is continuously supplied with an oxidant and a reductant so that it can deliver a current indefinitely. Fuel cell offer the possibility of achieving high thermodynamic efficiency in the conversion of Gibbs energy into mechanical work. Internal combustion engines at best convert only the fraction (T_(2)-T_(1))T_(2) of heat of combustion into mechanical work. While the thermodynamic efficiency of the fuel cell is give by, eta=(|DeltaG|)/(|DeltaH|) , where DeltaG is the Gibbs energy change for the cell reaction and DeltaH is the enthalpy change of the cell reaction. This efficiency can be upto 80%-90% also in contrast to normal heat engine efficiency which are generally about 40% Fuel cells may be classified according to the temperature range in wich they operate low temperature (25 to 100^(@)C ), medium temperature (100 to 500^(@)C) ), high temperature (500 "to" 1000^(@)C) and very high temperature is that catalyst for the various steps in the process are not so necessary. Polarization of a fuel cell reduces the current. Polarization is the result of slow reactions or processes such as diffusion in the cell. The figure indicates the construction of hydrogen-oxygen fuel cell with a solid electrolyte, which is an ion exchange membrane. The membrane is impermeable to the reactant gases, but is permeable to hydrogen ions, which carry the current between the electrodes. To facillitate the operation finely divided platinum that function as a catalyst. Water is drained out of the cell during operation. Fuel cells of this general type have been used successfully in the space program and are quite efficient. their disadvantages for large-scale commercial application are that hydrogen presetns storage problems, and platinum is an expensive catalyst. Cheaper catalysts have been found for higher temperature operatureof hydrogen-oxygen fuel cells. Fuel cells taht use hydrocarbons and air have been developed, but their power per unit weight is too low to make them practical in ordinary automobiles. Better catalysts are needed. A hydrogen-oxygen fuel cell may hae an acidic or alkaline electrolyte. The half-cell reactions are: (1)/(2)O_(2)(g)+2H^(+)+2e^(-)rarrH_(2)O(l) E^(@)=1.2288V 2H^(+)+2e^(-)rarrH_(2)(g)E^(@)=0 H_(2)(g)+(1)/(2)O_(2)(g)rarrH_(2)O(l) E^(@)=1.2288V or (1)/(2)O_(2)(g)+H_(2)O(g)+2e^(-)rarr2OH^(-) E^(@)=0.4009V 2H_(2)O(l)+2e^(-)rarrH_(2)(g)+2OH^(-)E^(@)=-0.8279V H_(2)(g)+(1)/(2)O_(2)(g)rarrH_(2)O(l) E^(@)=1.2288V To maximize the power per unit mass of an electrochemical cell, the electronic and electrolytic resistances of the cell must be minimized. than aqueous solutions, high-temperature electrochemical cells are of special interest for practical applications. High temperature also allow the use of liquid metal electrode, which makes possibel high current densities than solid electrodes. Why are fuel cells not being used in daily life depite their very high efficiency?