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If during an isothermal process certain ...

If during an isothermal process certain gas is expanded from `V_(1)` to `V_(2)` . Then, which of the following would be true?

A

during expansion temperature of the gas remains fixed

B

internal energy of the gas remains fixed

C

enthalpy of the gas remains fixed

D

entropy of the gas remains fixed

Text Solution

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The correct Answer is:
To solve the problem of determining which statements are true during an isothermal expansion of a gas from volume \( V_1 \) to \( V_2 \), we will analyze each option based on the principles of thermodynamics. ### Step-by-Step Solution: 1. **Understanding Isothermal Process**: - An isothermal process is defined as a thermodynamic process that occurs at a constant temperature. For an ideal gas, this means that the temperature does not change throughout the expansion or compression. **Hint**: Recall that in an isothermal process, the internal energy change (\( \Delta U \)) is zero for an ideal gas. 2. **Applying the Ideal Gas Law**: - The ideal gas law is given by the equation \( PV = nRT \). Since the temperature \( T \) is constant during an isothermal process, we can express the relationship between the initial and final states of the gas as: \[ P_1 V_1 = P_2 V_2 \] - Here, \( P_1 \) and \( P_2 \) are the pressures at volumes \( V_1 \) and \( V_2 \), respectively. **Hint**: Remember that for an ideal gas, if temperature is constant, the product of pressure and volume remains constant. 3. **Evaluating Each Statement**: - **Option A**: During expansion, the temperature of the gas remains fixed. - **True**: This is the definition of an isothermal process. - **Option B**: The internal energy of the gas remains fixed. - **False**: While the change in internal energy (\( \Delta U \)) is zero, this does not mean that the internal energy itself is fixed. It can have a specific value depending on the temperature. - **Option C**: The enthalpy of the gas remains fixed. - **False**: Enthalpy (\( H \)) is defined as \( H = U + PV \). Since \( P \) and \( V \) change during the process, the enthalpy will also change unless both \( P \) and \( V \) change in such a way that their product remains constant, which is not guaranteed in an isothermal process. - **Option D**: The entropy of the gas remains fixed. - **False**: Entropy (\( S \)) is a measure of the disorder or randomness of a system. During the expansion from \( V_1 \) to \( V_2 \), the volume increases, leading to an increase in entropy as the gas particles have more space to occupy. **Hint**: Consider how changes in volume affect the randomness and disorder of the gas particles. 4. **Conclusion**: - The only true statement during the isothermal expansion of the gas from \( V_1 \) to \( V_2 \) is that the temperature of the gas remains fixed. ### Final Answer: **Option A** is the only correct answer.
To solve the problem of determining which statements are true during an isothermal expansion of a gas from volume \( V_1 \) to \( V_2 \), we will analyze each option based on the principles of thermodynamics. ### Step-by-Step Solution: 1. **Understanding Isothermal Process**: - An isothermal process is defined as a thermodynamic process that occurs at a constant temperature. For an ideal gas, this means that the temperature does not change throughout the expansion or compression. **Hint**: Recall that in an isothermal process, the internal energy change (\( \Delta U \)) is zero for an ideal gas. ...
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