WBJEE · Physics · Thermodynamics
The initial pressure and volume of a given mass of an ideal gas \(\left(\right.\) with \(\frac{C_{p}}{C_{V}}=\gamma),\) taken in a cylinder fitted with a piston, are \(p_{0}\) and \(V_{0}\) respectively. At this stage the gas has the same temperature as that of the surrounding medium which is \(T_{0}\). It is adiabatically compressed to a volume equal to \(\frac{V_{0}}{2}\) Subsequently the gas is allowed to come to thermal equilibrium with the surroundings. What is the heat released to the surrounding?
- A 0
- B \((2^{\gamma-1}-1) \frac{p_{0} V_{0}}{\gamma-1}\)
- C \(\gamma {p_{0}} {V_{0}} ln2\)
- D \(\frac{{p_{0}} V_{0}}{2(\gamma-1)}\)
Answer & Solution
Correct Answer
(B) \((2^{\gamma-1}-1) \frac{p_{0} V_{0}}{\gamma-1}\)
Step-by-step Solution
Detailed explanation
The equation of state for an ideal gas undergoing adiabatic process is given as, \[ T V^{\gamma-1}=\text { constant } \] Let the temperature after adiabatic compression as given in the question be \(T\) then, \[ T_{0} V^{\gamma-1}=T\left(\frac{V_{0}}{2}\right)^{\gamma-1} \]…
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