The P-V diagram of 2,g of helium gas for a ce | vedclass

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

Question

(B) For a monoatomic gas like helium,the molar heat capacity at constant volume is $C_V = \frac{3}{2}R$.The work done $W$ during the process $A 	o B$

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(B) For a monoatomic gas like helium,the molar heat capacity at constant volume is $C_V = \frac{3}{2}R$.The work done $W$ during the process $A 	o B$ is the area under the $P-V$ curve,which is a trapezoid:$W = \frac{1}{2} 	imes (P_A + P_B) 	imes (V_B - V_A) = \frac{1}{2} 	imes (P_0 + 2P_0) 	imes (2V_0 - V_0) = \frac{1}{2} 	imes 3P_0 	imes V_0 = 1.5 P_0 V_0$.Using the ideal gas law $PV = nRT$,we find the change in internal energy $\Delta U = n C_V \Delta T = n (\frac{3}{2}R) \Delta T = \frac{3}{2} (nR \Delta T) = \frac{3}{2} (P_B V_B - P_A V_A)$.Substituting the values: $\Delta U = \frac{3}{2} ((2P_0)(2V_0) - (P_0)(V_0)) = \frac{3}{2} (4P_0V_0 - P_0V_0) = \frac{3}{2} (3P_0V_0) = 4.5 P_0 V_0$.According to the first law of thermodynamics,the heat given $\Delta Q = \Delta U + W$.$\Delta Q = 4.5 P_0 V_0 + 1.5 P_0 V_0 = 6 P_0 V_0$.

The $P-V$ diagram of $2\,g$ of helium gas for a certain process $A \to B$ is shown in the figure. What is the heat given to the gas during the process $A \to B$ (in $P_0V_0$)?

Similar Questions

In the circuit shown,the readings of the ammeter and voltmeter are $4\,A$ and $20\,V$ respectively. The meters are non-ideal. Then $R$ is:

$A$ committee of $12$ members is to be formed from $9$ women and $8$ men. The number of committees in which the women are in majority is

The equation of the normal to the curve $y=x \log x$,which is parallel to the line $2x-2y+3=0$,is

If $4$ moles of an ideal monoatomic gas at temperature $400 ~K$ is mixed with $2$ moles of another ideal monoatomic gas at temperature $700 ~K$,the temperature of the mixture is

How are the following compounds related?

Vedclass Test Series

Exam Paper Generator

Online Exam Module