Question

In a given process of an ideal gas, $dW \,= \,0$ and $dQ < 0$. Then for the gas

• A. the temperature will decrease
• B. the volume will increase
• C. the pressure will remain constant
• D. the temperature will increase

Answer 1

Answer: (A)

the temperature will decrease

Answer 2

From first law of thermodynamics,
\hspace15mm dQ = dU + dW
\hspace15mm dQ = dU, if dW = 0
Since $\, \, \, \, \, \, \, \, \, \, \, \, \,$dQ< O
Therefore $\, \, \, \, \, \, \, \, \, \, \, \, \,$ dU < 0
or $\, \, \, \, \, \, \, \, \, \, \, U_{final} < U_{initial}$
or temperature will decrease.
NOTE Internal energy U of an ideal gas depends only on the temperature of the gas. Internal energy of n moles of an ideal gas is given by
U = r(f/2)RT
U $?$T
Here, f is the degree of freedom of the gas