1
JEE Main 2020 (Online) 7th January Evening Slot
+4
-1
Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperature, T1 and T2 . The temperature of the hot reservoir of the first engine is T1 and the temperature of the cold reservoir of the second engine is T2 . T is temperature of the sink of first engine which is also the source for the second which is also the source for the second engine. How is T related to T1 and T2 . If both engines perform equal amount of work?
A
$$T = {{2{T_1}{T_2}} \over {{T_1} + {T_2}}}$$
B
$$T = \sqrt {{T_1}{T_2}}$$
C
$$T = {{{T_1} + {T_2}} \over 2}$$
D
T = 0
2
JEE Main 2020 (Online) 7th January Evening Slot
+4
-1
Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently the mean collision time between the gas molecule changes from $${\tau _1}$$ to $${\tau _2}$$ . If $${{{C_p}} \over {{C_v}}} = \gamma$$ for this gas then a good estimate for $${{{\tau _2}} \over {{\tau _1}}}$$ is given by :
A
$${\left( 2 \right)^{{{1 + \gamma } \over 2}}}$$
B
2
C
$${\left( {{1 \over 2}} \right)^{{{1 + \gamma } \over 2}}}$$
D
$${\left( {{1 \over 2}} \right)^\gamma }$$
3
JEE Main 2020 (Online) 7th January Morning Slot
+4
-1
Two moles of an ideal gas with $${{{C_P}} \over {{C_V}}} = {5 \over 3}$$ are mixed with 3 moles of another ideal gas with $${{{C_P}} \over {{C_V}}} = {4 \over 3}$$. The value of $${{{C_P}} \over {{C_V}}}$$ for the mixture is :
A
1.50
B
1.45
C
1.47
D
1.42
4
JEE Main 2020 (Online) 7th January Morning Slot
+4
-1
A litre of dry air at STP expands adiabatically to a volume of 3 litres. If $$\gamma$$ = 1.40, the work done by air is : (31.4 = 4.6555) [Take air to be an ideal gas]
A
60.7 J
B
100.8 J
C
90.5 J
D
48 J
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