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

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(B) For Helium (a monoatomic gas),the degrees of freedom $f = 3$.The change in internal energy $\Delta U$ is given by:$\Delta U = \frac{f}{2} \Delta(P

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(B) For Helium (a monoatomic gas),the degrees of freedom $f = 3$.The change in internal energy $\Delta U$ is given by:$\Delta U = \frac{f}{2} \Delta(PV) = \frac{3}{2} (P_B V_B - P_A V_A)$From the graph,$P_A = P_0, V_A = V_0$ and $P_B = 2P_0, V_B = 2V_0$.$\Delta U = \frac{3}{2} (2P_0 \cdot 2V_0 - P_0 \cdot V_0) = \frac{3}{2} (4P_0 V_0 - P_0 V_0) = \frac{3}{2} (3P_0 V_0) = 4.5 P_0 V_0$.The work done $W$ by the gas is equal to the area under the $P-V$ curve,which is a trapezium:$W = 	ext{Area} = \frac{1}{2} 	imes (P_A + P_B) 	imes (V_B - V_A)$$W = \frac{1}{2} 	imes (P_0 + 2P_0) 	imes (2V_0 - V_0) = \frac{1}{2} 	imes (3P_0) 	imes (V_0) = 1.5 P_0 V_0$.From the first law of thermodynamics,the total heat given $\Delta Q$ is:$\Delta Q = \Delta U + W$$\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 $,P_0V_0$)?

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