SATHEE: Heat and Thermodynamics 1 Question 4

Heat and Thermodynamics 1 Question 4

4. In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation $V T = k$ , where $k$ is a constant. In this process, the temperature of the gas is increased by $Δ T$ . The amount of heat absorbed by gas is (where, $R$ is gas constant)

(2019 Main, 11 Jan II)

(a) $\frac{1}{2} k R Δ T$

(b) $\frac{2 k}{3} Δ T$

(d) $\frac{3}{2} R Δ T$

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Solution:

Given, $V T = k$ , $(k$ is constant $)$

$or T \propto \frac{1}{V}$

Using ideal gas equation,

$\begin{array}{ll} p V = n R T \\ p V \propto T \\ \Rightarrow & p V \propto \frac{1}{V} \\ or & p V^{2} = constant \end{array}$

i.e a polytropic process with $x = 2$ .

(Polytropic process means, $p V^{x} =$ constant)

We know that, work done in a polytropic process is given by

$Δ W = \frac{p_{2} V_{2} - p_{1} V_{1}}{1 - x} (for x \neq 1)$

and, $Δ W = p V \ln (\frac{V_{2}}{V_{1}}) ($ for $x = 1)$

Here, $x = 2$ ,

$\begin{array}{ll} ∴ & Δ W = \frac{p_{2} V_{2} - p_{1} V_{1}}{1 - x} = \frac{n R (T_{2} - T_{1})}{1 - x} \\ \Rightarrow & Δ W = \frac{n R Δ T}{1 - ‘ 2} = - n R Δ T \end{array}$

Now, for monoatomic gas change in internal energy is given by

$Δ U = \frac{3}{2} R Δ T$

Using first law of thermodynamics, heat absorbed by one mole gas is

$\begin{aligned} Δ Q & = Δ W + Δ U = \frac{3}{2} R Δ T - R Δ T \\ \Rightarrow Δ Q & = \frac{1}{2} R Δ T \end{aligned}$

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Heat and Thermodynamics 1 Question 4

4. In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation $V T = k$ , where $k$ is a constant. In this process, the temperature of the gas is increased by $Δ T$ . The amount of heat absorbed by gas is (where, $R$ is gas constant)

Solution:

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सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Heat and Thermodynamics 1 Question 4

4. In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation VT=k, where k is a constant. In this process, the temperature of the gas is increased by ΔT. The amount of heat absorbed by gas is (where, R is gas constant)

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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4. In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation $V T = k$ , where $k$ is a constant. In this process, the temperature of the gas is increased by $Δ T$ . The amount of heat absorbed by gas is (where, $R$ is gas constant)