One mole of an ideal gas passes through a process where pressure and volume obey the pressure . Here and are constants. Calculate the change in the temperature of the gas, if its volume changes from to .

Question

One mole of an ideal gas passes through a process where pressure and volume obey the pressure $P = P_{0} [1 - \frac{1}{2} {(\frac{V_{0}}{V})}^{2}]$ . Here $P_{0}$ and $V_{0}$ are constants. Calculate the change in the temperature of the gas, if its volume changes from $V_{0}$ to $2 V_{0}$ .

Smart Achievers · Accepted Answer

(2)

We have given, $P = P_{0} [1 + \frac{1}{2} {(\frac{V_{0}}{V})}^{2}]$

When $V_{1} = V_{0}$ $\Rightarrow P_{1} = P_{0} [1 - \frac{1}{2}] = \frac{P_{0}}{2}$

When $V_{2} = 2 V_{0}$

$Δ T =$ $| (\frac{1}{n R}) (P_{1} V_{1} - P_{2} V_{2}) |$ $= (\frac{1}{n R})$ $| (\frac{P_{0} V_{0}}{2} - \frac{7 P_{0} V_{0}}{4}) |$ $= \frac{5 P_{0} V_{0}}{4 n R} = \frac{5 P_{0} V_{0}}{4 R}$ $(∵ n = 1)$

Solution

Q.
One mole of an ideal gas passes through a process where pressure and volume obey the pressure $P = P_{0} [1 - \frac{1}{2} {(\frac{V_{0}}{V})}^{2}]$ . Here $P_{0}$ and $V_{0}$ are constants. Calculate the change in the temperature of the gas, if its volume changes from $V_{0}$ to $2 V_{0}$ .

1 $\frac{1}{2} \frac{P_{0} V_{0}}{R}$

2 $\frac{5}{4} \frac{P_{0} V_{0}}{R}$

3 $\frac{3}{4} \frac{P_{0} V_{0}}{R}$

4 $\frac{1}{4} \frac{P_{0} V_{0}}{R}$

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Solution

Q. One mole of an ideal gas passes through a process where pressure and volume obey the pressure P=P0[1-12(V0V)2]. Here P0 and V0 are constants. Calculate the change in the temperature of the gas, if its volume changes from V0 to 2V0.

1 12P0V0R

2 54P0V0R

3 34P0V0R

4 14P0V0R