Certain amount of heat supplied to an ideal gas under isothermal conditions will result in

Options

A. rise in temperature q
B. doing external work and a change in temperature
C. doing external work
D. an increase in the internal energy of the gas

Answer

To solve the question regarding the effect of heat supplied to an ideal gas under isothermal conditions, we can follow these steps:

### Step 1: Understand Isothermal Process
An isothermal process is one where the temperature of the system remains constant. For an ideal gas, this means that any heat added to the system does not change the internal energy of the gas.

**Hint:** Remember that in an isothermal process, the temperature (T) is constant.

### Step 2: Apply the First Law of Thermodynamics
The first law of thermodynamics states:
\[ \Delta Q = \Delta U + \Delta W \]
Where:
- \(\Delta Q\) is the heat added to the system.
- \(\Delta U\) is the change in internal energy.
- \(\Delta W\) is the work done by the system.

**Hint:** This law helps us relate heat, internal energy, and work done.

### Step 3: Analyze Internal Energy Change
For an ideal gas, the internal energy (\(U\)) is a function of temperature. Since the temperature remains constant in an isothermal process, the change in internal energy is zero:
\[ \Delta U = 0 \]

**Hint:** Recall that for an ideal gas, internal energy depends solely on temperature.

### Step 4: Substitute Values in the First Law
Substituting \(\Delta U = 0\) into the first law equation:
\[ \Delta Q = 0 + \Delta W \]
This simplifies to:
\[ \Delta Q = \Delta W \]
This means that all the heat supplied to the gas is converted into work done by the gas.

**Hint:** This shows that the heat added goes entirely into doing work.

### Step 5: Conclusion
Since the heat supplied results in work done and does not change the internal energy or temperature, the correct answer to the question is that the heat supplied to the ideal gas under isothermal conditions will result in doing external work.

**Final Answer:** The correct option is C: doing external work.