SATHEE: Heat and Thermodynamics 4 Question 3

Heat and Thermodynamics 4 Question 3

3. One mole of an ideal gas passes through a process, where pressure and volume obey the relation $p = p_{0} [1 - \frac{1}{2} {(\frac{V_{0}}{V})}^{2}]$ .

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 $2 V_{0}$ .

(a) $\frac{1}{2} \frac{p_{0} V_{0}}{R}$

(b) $\frac{1}{4} \frac{p_{0} V_{0}}{R}$

(d) $\frac{5}{4} \frac{p_{0} V_{0}}{R}$

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Solution:

Given process equation for 1 mole of an ideal gas is

$p = p_{0} (1 - \frac{1}{2} {(\frac{V_{0}}{V})}^{2})$

Also, for 1 mole of ideal gas,

$\begin{aligned} p V = R T \\ ∴ & p = \frac{R T}{V} \end{aligned}$

So, from Eqs. (i) and (ii), we have

$\begin{aligned} \frac{R T}{V} & = p_{0} (1 - \frac{1}{2} {(\frac{V_{0}}{V})}^{2}) \\ ∴ & T & = \frac{p_{0} V}{R} (1 - \frac{1}{2} {(\frac{V_{0}}{V})}^{2}) \end{aligned}$

When volume of gas is $V_{0}$ , then by substituting $V = V_{0}$ in Eq. (iii), we get

Temperature of gas is

$T_{1} = \frac{p_{0} V_{0}}{R} (1 - \frac{1}{2} {(\frac{V_{0}}{V_{0}})}^{2}) = \frac{p_{0} V_{0}}{2 R}$

Similarly, at volume, $V = 2 V_{0}$

Temperature of gas is

$T_{2} = \frac{p_{0} (2 V_{0})}{R} (1 - \frac{1}{2} {(\frac{V_{0}}{2 V_{0}})}^{2}) = \frac{7}{4} \frac{p_{0} V_{0}}{R}$

So, change in temperature as volume changes from $V_{0}$ to $2 V_{0}$ is

$Δ T = T_{2} - T_{1} = (\frac{7}{4} - \frac{1}{2}) \frac{p_{0} V_{0}}{R} = \frac{5}{4} \frac{p_{0} V_{0}}{R}$

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Heat and Thermodynamics 4 Question 3

3. One mole of an ideal gas passes through a process, where pressure and volume obey the relation $p = p_{0} [1 - \frac{1}{2} {(\frac{V_{0}}{V})}^{2}]$ .

Solution:

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Heat and Thermodynamics 4 Question 3

3. One mole of an ideal gas passes through a process, where pressure and volume obey the relation p=p0[1−12(V0V)2].

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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3. One mole of an ideal gas passes through a process, where pressure and volume obey the relation $p = p_{0} [1 - \frac{1}{2} {(\frac{V_{0}}{V})}^{2}]$ .