Heat & Thermodynamics · JEE Main previous year questions

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2021 14 questions

Q372021 · 1 Sept 2021 · Shift 2
Due to cold weather a $1 m$ water pipe of cross-sectional area $1 c m^{2}$ is filled with ice at $- 1 0^{\circ} C$ . Resistive heating is used to melt the ice. Current of $0.5 A$ is passed through $4 kΩ$ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required? (Given latent heat of fusion for water/ice $= 3.33 \times 1 0^{5} J k g^{- 1}$ , specific heat of ice $= 2 \times 1 0^{3} J k g^{- 1}$ and density of ice $= 1 0^{3} kg/ m^{3}$ )
1. A. $0.353 s$
2. B. $35.3 s$
3. C. $3.53 s$
4. D. $70.6 s$
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Answer: B
Q502021 · 26 Aug 2021 · Shift 2
A refrigerator consumes an average 35W power to operate between temperature $- 1 0^{\circ} C$ to $2 5^{\circ} C$ . If there is no loss of energy then how much average heat per second does it transfer?
1. A. $263 J/s$
2. B. $298 J/s$
3. C. $350 J/s$
4. D. $35 J/s$
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Answer: A
Q342021 · 27 Jul 2021 · Shift 2
One mole of an ideal gas is taken through an adiabatic process where the temperature rises from $2 7^{\circ}$ C to $3 7^{\circ}$ C. If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the following is true? [R = 8.314 J $mo l^{- 1} K^{- 1}$ ]
1. A.work done by the gas is close to 332 J
2. B.work done on the gas is close to 582 J
3. C.work done by the gas is close to 582 J
4. D.work done on the gas is close to 332 J
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Answer: B
Q492021 · 27 Jul 2021 · Shift 2
Two Carnot engines A and B operate in series such that engine A absorbs heat at $T_{1}$ and rejects heat to a sink at temperature T. Engine B absorbs half of the heat rejected by Engine A and rejects heat to the sink at $T_{3}$ . When workdone in both the cases is equal, to value of T is :
1. A. $\frac{2}{3} T_{1} + \frac{3}{2} T_{3}$
2. B. $\frac{1}{3} T_{1} + \frac{2}{3} T_{3}$
3. C. $\frac{3}{2} T_{1} + \frac{1}{3} T_{3}$
4. D. $\frac{2}{3} T_{1} + \frac{1}{3} T_{3}$
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Answer: D
Q312021 · 25 Jul 2021 · Shift 1
For a gas $C_{P} - C_{V} = R$ in a state P and $C_{P} - C_{V} = 1.10 R$ in a state Q, $T_{P}$ and $T_{Q}$ are the temperatures in two different states P and Q respectively. Then
1. A. $T_{P} = T_{Q}$
2. B. $T_{P} < T_{Q}$
3. C. $T_{P} = 0.9 T_{Q}$
4. D. $T_{P} > T_{Q}$
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Answer: D
Q382021 · 25 Jul 2021 · Shift 1
A monoatomic ideal gas, initially at temperature $T_{1}$ is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_{2}$ by releasing the piston suddenly. If $l_{1}$ and $l_{2}$ are the lengths of the gas column, before and after the expansion respectively, then the value of $\frac{T _{1}}{T _{2}}$ will be :
1. A. $(\frac{l _{1}}{l _{2}})^{\frac{2}{3}}$
2. B. $(\frac{l _{2}}{l _{1}})^{\frac{2}{3}}$
3. C. $\frac{l _{2}}{l _{1}}$
4. D. $\frac{l _{1}}{l _{2}}$
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Answer: B
Q432021 · 25 Jul 2021 · Shift 1
1. A. $\frac{8}{3}$
2. B. $\frac{3}{8}$
3. C. $\frac{3}{4}$
4. D. $\frac{4}{3}$
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Answer: B
Q412021 · 25 Jul 2021 · Shift 2
Two spherical soap bubbles of radii $r_{1}$ and $r_{2}$ in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to :
1. A. $\frac{r _{1} r _{2}}{r _{1} + r _{2}}$
2. B. $r_{1} r_{2}$
3. C. $r_{1}^{2} + r_{2}^{2}$
4. D. $\frac{r _{1} + r _{2}}{2}$
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Answer: C
Q482021 · 25 Jul 2021 · Shift 2
A heat engine has an efficiency of $\frac{1}{6}$ . When the temperature of sink is reduced by $6 2^{\circ} C$ , its efficiency gets doubled. The temperature of the source is :
1. A. $12 4^{\circ} C$
2. B. $3 7^{\circ} C$
3. C. $6 2^{\circ} C$
4. D. $9 9^{\circ} C$
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Answer: D
Q362021 · 18 Mar 2021 · Shift 1
1. A. $- 500 J$
2. B. $- 400 J$
3. C. $400 J$
4. D. $200 J$
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Answer: A
Q442021 · 18 Mar 2021 · Shift 2
For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where $γ$ is the ratio of specific heats) :
1. A. $- \frac{1}{γ} \frac{d V}{V}$
2. B. $- γ \frac{V}{d V}$
3. C. $- γ \frac{d V}{V}$
4. D. $\frac{d V}{V}$
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Answer: C
Q382021 · 16 Mar 2021 · Shift 1
In thermodynamics, heat and work are :
1. A.Path functions
2. B.Point functions
3. C.Extensive thermodynamics state variables
4. D.Intensive thermodynamic state variables
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Answer: A
Q402021 · 25 Feb 2021 · Shift 2
1. A. $2$
2. B. $\frac{1}{2}$
3. C. $\frac{1}{2}$
4. D.2
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Answer: A
Q602021 · 25 Feb 2021 · Shift 2· Numerical answer
A reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced by 52K, its efficiency is doubled. The temperature in Kelvin of the source will be __________.
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Answer: 208