Two cylinders A and B fitted with pistons con | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) For an ideal diatomic gas,the molar heat capacity at constant pressure is $C_p$ and at constant volume is $C_v$. The ratio is given by $\gamma = \

Vedclass · Accepted Answer

$42$

Vedclass · Answer

(D) For an ideal diatomic gas,the molar heat capacity at constant pressure is $C_p$ and at constant volume is $C_v$. The ratio is given by $\gamma = \frac{C_p}{C_v} = 1.4$.In cylinder $A$,the piston is free to move,so the process is isobaric (constant pressure). The heat supplied is $\Delta Q = \mu C_p (\Delta T)_A$.In cylinder $B$,the piston is fixed,so the process is isochoric (constant volume). The heat supplied is $\Delta Q = \mu C_v (\Delta T)_B$.Since the same amount of heat is given to both,we have $\mu C_p (\Delta T)_A = \mu C_v (\Delta T)_B$.Rearranging for $(\Delta T)_B$,we get $(\Delta T)_B = \frac{C_p}{C_v} (\Delta T)_A = \gamma (\Delta T)_A$.Substituting the given values: $(\Delta T)_B = 1.4 	imes 30 \ K = 42 \ K$.

Column $-I$	Column $-II$
$(a)$ Isothermal process	$(i)$ $W = \frac{\mu R(T_1 - T_2)}{\gamma - 1}$
$(b)$ Adiabatic process	$(ii)$ $W = P\Delta V$
	$(iii)$ $W = 2.303\mu RT \log_{10} \left( \frac{V_2}{V_1} \right)$

Similar Questions

$A$ thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $1.4$. The vessel is moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surroundings,the temperature of the gas increases by ... ($R =$ universal gas constant)

One mole of a diatomic ideal gas undergoes a cyclic process $ABC$ as shown in the figure. The process $BC$ is adiabatic. The temperatures at $A, B$ and $C$ are $400 \ K, 800 \ K$ and $600 \ K$ respectively. Choose the correct statement.

The ratio of the work done, change in internal energy, and heat absorbed when a diatomic gas expands at constant pressure is

$A$ monoatomic gas of pressure $P$ having volume $V$ expands isothermally to a volume $2V$ and then adiabatically to a volume $16V$. The final pressure of the gas is (ratio of specific heats $\gamma = \frac{5}{3}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module