2 moles of a monoatomic gas are expanded to d | vedclass

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

Question

(B) Given: $n = 2$, $V_f = 2V_i$, $T_i = 300\, K$, process $P/V = k$ (polytropic index $x = -1$).Using $PV = nRT$ and $P = kV$, we get $kV^2 = nRT$, s

Vedclass · Accepted Answer

$\Delta Q = 3200\, R$

Vedclass · Answer

(B) Given: $n = 2$, $V_f = 2V_i$, $T_i = 300\, K$, process $P/V = k$ (polytropic index $x = -1$).Using $PV = nRT$ and $P = kV$, we get $kV^2 = nRT$, so $T \propto V^2$.$T_f = T_i (V_f/V_i)^2 = 300 	imes (2)^2 = 1200\, K$.Change in temperature $\Delta T = T_f - T_i = 1200 - 300 = 900\, K$. (Option $A$ is true).Work done $W = \int P dV = \int_V^{2V} kV dV = k [V^2/2]_V^{2V} = k/2 (4V^2 - V^2) = 3/2 kV^2 = 3/2 PV = 3/2 nRT$.At initial state, $W_i = 3/2 nRT_i = 3/2 	imes 2 	imes R 	imes 300 = 900\, R$. (Option $D$ is true).Change in internal energy $\Delta U = n C_v \Delta T = 2 	imes (3/2 R) 	imes 900 = 2700\, R$.Heat supplied $\Delta Q = \Delta U + W = 2700\, R + 900\, R = 3600\, R$. (Option $C$ is true).Since $\Delta Q = 3600\, R$, option $B$ is false.

$2$ moles of a monoatomic gas are expanded to double its initial volume, through a process $P/V = \text{constant}$. If its initial temperature is $300\, K$, then which of the following is not true?

Similar Questions

The graph of pressure $(P)$ and volume $(V)$ according to $PV^n = C$,where $n = 1.4$. Identify the correct graph.

$A$ monoatomic gas is taken through a process $TP^{-1/3} = \text{constant}$. If heat is given to the gas, what happens to its temperature?

One mole of an ideal monoatomic gas at temperature $T_0$ expands slowly according to the law $P = kV$ ($k$ is a constant). If the final temperature is $2T_0$,the heat supplied to the gas is:

An ideal gas with heat capacity at constant volume $C_V$ undergoes a quasistatic process described by $p V^{\alpha} = \text{constant}$ in a $p-V$ diagram,where $\alpha$ is a constant. The heat capacity of the gas during this process is given by

$1 \, \text{mole}$ of a gas expands with temperature as $V = KT^{2/3}$. What is the work done when temperature changes by $30^oC$ (in $R$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module