Verified Solution • 2025–26 Session moderate

QPages 77-80: Q30: HC Verma: Concepts of Physics - Volume 2 Specific Heat Capacities of Gases Pages 77-80: Q30 Solution: The figure shows an adiabatic cylindrical tube of volume…

The figure shows an adiabatic cylindrical tube of volume

V_0

divided in two parts by a frictionless adiabatic separator. Initially, the separator is kept in the middle, an ideal gas at pressure

p_1

and temperature

T_1

is injected into the left part and another ideal gas at pressure

p_2

and temperature

T_2

is injected into the right part.

C_p/C_v = \gamma

is the same for both the gases. The separator is slid slowly and is released at a position where it can stay in equilibrium. Find a) the volumes of the two parts b) the heat given to the gas in the left part and c) the final common pressure of the gases.

Step-by-Step Verified Solution

**Answer:** (a)

V_1 = V_0/2

,

V_2 = V_0/2

(b)

Q = 0

(c)

P = \frac{P_1 + P_2}{2}

. **Step-by-Step Explanation:** Adiabatic separator, so each side undergoes adiabatic process. Final equilibrium:

P_1' = P_2'

and

T_1' = T_2'

(from

TV^{\gamma-1}

relations). Solving gives

V_1 = V_0/2

,

V_2 = V_0/2

and final pressure

P = (P_1 + P_2)/2

.

All Questions in this Chapter

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