Pick out the incorrect statement among the following

Moderate

A

If the change in volume of an ideal gas system is zero then the work done by the gas is always zero
B

The specific heat of an ideal gas can be negative
C

Change in internal energy of an ideal gas in isothermal process is zero
D

In adiabatic expansion of ideal gas the internal energy of the gas decreases

Solution

1. In a cyclic process the change in volume is zero but work done is not zero so (1) is incorrect statement.
2. For a gas which obey’s $P V^{x} =$ constant
$C = \frac{R}{γ - 1} + \frac{R}{1 - x}$
We can see that x can have a range of values, which can make C negative. Hence it is correct.
3. $d U = n C_{v} d T$ , for an isothermal process, change in temperature is zero, hence there will be no change in internal energy.
4. Using first law of thermodynamics $d Q = d U + d W$ , for adiabatic process $d Q = 0$
Hence, $d U = - d W$ . Therefore, during expansion work done is positive, the internal energy decreases.
Therefore, the correct answer is $(A)$

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