Thermodynamics

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In Carnot engine efficiency is 40% at hot reservoir temperature T. For efficiency 50%, what will be temperature of hot reservoir?

$\frac{T}{5}$

$\frac{2 T}{5}$

6 T

$\frac{6 T}{5}$

Solution

$\frac{6 T}{5}$

The efficiency of a heat engine is defined as the ratio of work done to the heat supplied, ie,

$η = \frac{work done}{Heat input}$

= $\frac{W}{Q}$

⇒ $η = 1 - \frac{T_{2}}{T_{1}}$

where T₂ is temperature of sink, and T₁ is temperature of hot reservoir.

∴ $\frac{40}{100} = 1 - \frac{T_{2}}{T_{1}}$

⇒ $\frac{T_{2}}{T_{1}} = 0.6$

⇒ $T_{2} = 0.6 T_{1}$

Again, $\frac{50}{100} = 1 - \frac{T_{2}}{T_{1}'}$

⇒ $\frac{T_{2}}{T_{1}'} = 0.5$

⇒ $\frac{0.6 T_{1}}{T_{1}'} = 0.5$

∴ $T_{1}' = \frac{0.6}{0.5} T_{1}$

⇒ $T_{1}' = \frac{6}{5} T$

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Thermodynamics

In Carnot engine efficiency is 40% at hot reservoir temperature T. For efficiency 50%, what will be temperature of hot reservoir?

$\frac{T}{5}$

$\frac{2 T}{5}$

6 T

$\frac{6 T}{5}$

Some More Questions From Thermodynamics Chapter

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Two moles of helium gas are taken over the cycle ABCDA, as shown in the P–T diagram.

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When a system is taken from state i to state f along the path iaf, it is found that Q = 50 cal and W = 20 cal. Along the path’ ibf Q = 36 cal. W along the path ibf is

The work of 146 kJ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by 7° C. The gas is

(R = 8.3 J mol⁻¹ K⁻¹ )

Which of the following is incorrect regarding the first law of thermodynamics?

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For Daily Free Study Material Join wiredfaculty

Thermodynamics

In Carnot engine efficiency is 40% at hot reservoir temperature T. For efficiency 50%, what will be temperature of hot reservoir? T5 2 T5 6 T 6T5

Some More Questions From Thermodynamics Chapter

Two points P and Q are maintained at the potential of 10V and -4V respectively. The work done in moving 100 electrons from P to Q is

Two moles of helium gas are taken over the cycle ABCDA, as shown in the P–T diagram. Assuming the gas to be ideal the work done on the gas in taking it from A to B is

When a system is taken from state i to state f along the path iaf, it is found that Q = 50 cal and W = 20 cal. Along the path’ ibf Q = 36 cal. W along the path ibf is

The work of 146 kJ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by 7° C. The gas is(R = 8.3 J mol−1 K−1 )

Which of the following is incorrect regarding the first law of thermodynamics?

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Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

In Carnot engine efficiency is 40% at hot reservoir temperature T. For efficiency 50%, what will be temperature of hot reservoir?

$\frac{T}{5}$

$\frac{2 T}{5}$

6 T

$\frac{6 T}{5}$

Two moles of helium gas are taken over the cycle ABCDA, as shown in the P–T diagram.

Assuming the gas to be ideal the work done on the gas in taking it from A to B is

The work of 146 kJ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by 7° C. The gas is

(R = 8.3 J mol⁻¹ K⁻¹ )

A system goes from A to B via two processes I and II as shown in the figure. If ∆U₁ and ∆U₂ are the changes in internal energies in the processes I and II respectively, the