Thermodynamics (Physics) · Question 1

As shown in the figure, five Carnot engines, each with efficiency and same number of cycles per unit time, are operating between six heat reservoirs. The amount of heat released per cycle by one engine is completely absorbed by the next engine. Consider Q0 to be the amount of heat absorbed per cycle by the first engine and W as the amount of total work done by all the engines per cycle, then the net efficiency of the system is found to be net = WQ0 = 211243. The value of is: [figure]

Ten moles of an ideal monoatomic gas, initially in state a at atmospheric pressure and temperature Ta=27 , is enclosed in a metal cylinder of volume V0 fitted with a frictionless piston. The gas is suddenly compressed to state b with volume V0/3. Now, keeping the piston stationary, the cylinder is submerged in a water bath of temperature 11 until the gas reaches the temperature of the water bath, which is denoted as state c. Finally, while still in the water bath, the piston is brought slowly to its initial position, which is denoted as state f. If R is universal gas constant, then the correct option(s) is/are: [Given: 91/3=2.08]

1. The schematic P-V diagram of the processes described above is: [figure]
2. The change in internal energy in going from state a to b is 4860R.
3. The net change in the internal energy in the whole process is -240R.
4. The pressure and temperature of the state b are 2.08 times the atmospheric pressure and 624 K, respectively.

The efficiency of a Carnot engine operating with a hot reservoir kept at a temperature of 1000 K is 0.4. It extracts 150 J of heat per cycle from the hot reservoir. The work extracted from this engine is being fully used to run a heat pump which has a coefficient of performance 10. The hot reservoir of the heat pump is at a temperature of 300 K. Which of the following statements is/are correct:

1. Work extracted from the Carnot engine in one cycle is 60 J.
2. Temperature of the cold reservoir of the Carnot engine is 600 K.
3. Temperature of the cold reservoir of the heat pump is 270 K.
4. Heat supplied to the hot reservoir of the heat pump in one cycle is 540 J.

An ideal monatomic gas of n moles is taken through a cycle WXYZW consisting of consecutive adiabatic and isobaric quasi-static processes, as shown in the schematic V-T diagram. The volume of the gas at W, X and Y points are, 64 cm3, 125 cm3 and 250 cm3, respectively. If the absolute temperature of the gas TW at the point W is such that nRTW=1 J (R is the universal gas constant), then the amount of heat absorbed (in J) by the gas along the path XY is [figure]

One mole of a monatomic ideal gas undergoes the cyclic process J K L M J, as shown in the P-T diagram. [figure] Match the quantities mentioned in List-I with their values in List-II and choose the correct option. [ R is the gas constant.]

1. P → 1; Q → 3; R → 5; S → 4
2. P → 4; Q → 3; R → 5; S → 2
3. P → 4; Q → 1; R → 2; S → 2
4. P → 2; Q → 5; R → 3; S → 4