Name: Introduction to First Law of Thermodynamics
Uploaded: 2019-07-19
Duration: 7 min 10 s
Description: The video defines the first law of thermodynamics and explains the relation between the total kinetic energy and the internal energy of a gas. Watch on!

Question

$P - V$ diagram of an ideal gas for a process $A B C$ is as shown in the figure.

$(a)$ Find the change in internal energy of the gas during the process $A B C$ .
$(b)$ Find total heat absorbed or released by the gas during the process $A B C$ .
$(c)$ Plot pressure versus density graph of the gas for the process $A B C$ .

Accepted Answer

Solution for $(a)$ :

For an ideal gas, $P V = n R T$ ,

At state $A$ $(b)$

$A B C$

At state $C$ $\Rightarrow P_{C} V_{C} = n R T_{C}$

$\Rightarrow 3 P_{0} V_{0} = n R T_{C} . . . (2)$

From equations $(1)$ and $(2)$ , we can say,

$T_{A} = T_{C}$

Change in internal energy, $∆ U = n C_{v} ∆ T$

During the process $A B C$ ,

$∆ U = n C_{v} (T_{C} - T_{A})$

$∴ ∆ U = 0$

Solution for $(b)$ :

Work done in the process can be determined by measuring the area under the $P - V$ graph.

So, work done during the process $A B,$ $W_{AB} = - 2 P_{0} V_{0}$ and process $B C,$ $W_{BC} = 0$ .

Thus, the net work done in the process $A B C$ is

$W_{ABC} = W_{AB} + W_{BC}$

$\Rightarrow W_{ABC} = - 2 P_{0} V_{0}$ .

From first law of thermodynamics, heat exchange,

$Q = ∆ U + W$

Thus, the total heat exchange during the process $A B C$ is

$Q_{ABC} = 0 + (- 2 P_{0} V_{0})$

$∴ Q_{ABC} = - 2 P_{0} V_{0}$

Here, negative sign represents, the heat is released by the gas.

Solution for $(c)$ :

Mass of the gas, $m = ρ V$

where $ρ$ is the density and $V$ is the volume of the gas.

Since the mass of a gas remains constant during the processes,

$ρ \propto \frac{1}{V}$

In process $A B$ , $ρ$ will increase as $V$ decreases at constant pressure and in process $B C$ , $ρ$ is constant as $V$ is constant.

Thus, the $P - ρ$ graphs for this process $A B C$ is

Important Questions on Laws of Thermodynamics

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P-V diagram of an ideal gas for a process ABC is as shown in the figure. (a) Find the change in internal energy of the gas during the process ABC. (b) Find total heat absorbed or released by the gas during the process ABC. (c) Plot pressure versus density graph of the gas for the process ABC.

Important Questions on Laws of Thermodynamics

Learn and Prepare for any exam you want !