A carnot's reversible engine converts \[\frac{1}{6}th\] of heat input into work. When the temperature of sink is reduced 62 K, the efficiency of carnot's cycle, becomes \[\frac{1}{3}.\] Calculate temperature of source and sink
A diesel engine takes in 5 moles of air at \[20{}^\circ C\] and 1 atm, and compresses it adiabatically to \[\frac{1}{10}\text{th}\] of the original volume. If air is diatomic then work done and change in internal energy is
Three moles of an ideal monoatomic gas perform a cycle shown in figure. The gas temperatures in different states are \[{{T}_{1}}=200K,{{T}_{2}}=400K,{{T}_{3}}=1600K\] and \[{{T}_{4}}=800K.\] The work done by the gas during the cycle is (Take \[R=25/3\text{ }J/mol\text{-}K\])
The molar heat capacity of a certain substance varies with temperature according to the given equation, \[C=27.2+(4\times {{10}^{-3}})T.\] The heat necessary to change the temperature of 2 mol. of the substance from 300K to 700K is
A system changes from the state \[({{P}_{1}},\,\,\,{{V}_{1}})\] to \[({{P}_{2}},\,\,\,{{V}_{2}})\] as shown in the figure below. What is the work done by the system?
A diatomic ideal gas is heated at constant volume until the pressure is doubled and again heated at constant pressure until volume is doubled. The average molar heat capacity for whole process is:
An ideal monoatomic gas is confined in a cylinder, fitted with piston, which is connected to spring as shown in figure. The gas is heated by a-small electric heater until the piston moves out slowly by 0.1 m. Find the work done by the gas. Spring constant = 8000 N/m,-piston area \[=8\times {{10}^{-3}}{{\text{m}}^{2}}\] atmospheric pressure \[={{10}^{5}}Pa\].
Two carnots engines A and B are operated in series. The first one A receives heat at 1200 K and rejects to a reservoir at T and K. The second engine B receives the heat rejected by the first engine and in turn rejects to a heat reservoir at 300 K. Calculate the value of T, when work outputs of the two engines are equal.
DIRECTION: Read the passage given below and answer the questions that follows:
In the figure n mole of a monoatomic ideal gas undergo the process ABC as shown in the P-V diagram. The process AB is isothermal and BC is isochoric. The temperature of the gas at A is \[{{T}_{0}}\]. Total heat given to the gas during the process ABC is measured to be Q.
DIRECTION: Read the passage given below and answer the questions that follows:
In the figure n mole of a monoatomic ideal gas undergo the process ABC as shown in the P-V diagram. The process AB is isothermal and BC is isochoric. The temperature of the gas at A is \[{{T}_{0}}\]. Total heat given to the gas during the process ABC is measured to be Q.
DIRECTION: Read the passage given below and answer the questions that follows:
In the figure n mole of a monoatomic ideal gas undergo the process ABC as shown in the P-V diagram. The process AB is isothermal and BC is isochoric. The temperature of the gas at A is \[{{T}_{0}}\]. Total heat given to the gas during the process ABC is measured to be Q.
The average molar heat capacity of the gas in process ABC
A gas expands adiabatically at constant pressure such that its temperature \[T\,\propto \,a/\sqrt{V}.\] The value of \[\gamma =({{C}_{p}}/{{C}_{V}})\] of the gas is
For a certain process the molar heat capacity of an ideal gas is found to be \[\left( {{C}_{v}}+\frac{R}{2} \right).\] For the given process it can be concluded that
2 moles of a mono-atomic gas undergo isobaric expansion as shown in figure. The efficiency for the process is found to be \[\frac{x}{10}\]. Find the value of\[x\].
A 100 kg piston encloses 32 g of oxygen gas at a temperature of \[{{27}^{o}}C\] in a vertical cylinder of base area of \[4\text{ }d{{m}^{2}}\]. The air pressure outside is \[1\times {{10}^{5}}Pa\]. The axis of the cylinder is vertical, and the piston can move in it without friction. How much heat is to be transferred to the gas to raise the piston by 20 cm. Use \[R=\frac{25}{3}J/mol/K\]
An ideal refrigerator has a freezer at a temperature of \[-13{}^\circ C\]. The coefficient of performance of the engine is 5. The temperature of the air (to which heat is rejected) is.
The degrees of freedom per molecule of an ideal gas is 5. Work done by the gas is 100 J when it expands isobarically. The heat absorbed by the gas will be
Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature \[{{T}_{0}},\] While Box B contains one mole of helium at temperature (7/3) \[{{T}_{0}}\]. The boxes are then put into thermal contact with each other and heat flows between them until the gases reach a common final temperature (Ignore the heat capacity of boxes). Then, the final temperature of the gases, \[{{T}_{f}},\] in term of \[{{T}_{0}}\] is
743 J of heat energy is added to raise the temperature of 5 mole of an ideal gas by 2 K at constant pressure. How much heat energy is required to raise the temperature of the same mass of the gas by 2 K at constant volume?
A certain mass of gas is taken from an initial thermodynamic state A to another state B by process I and II. In process I the gas does 5 joules of work and absorbs 4 joules of heat energy. In process II, the gas absorbs 5 joules of heat. The work done by the gas in process II (see figure) is
Two vessels A and B contain water at temperature \[{{T}_{A}}\] and \[{{T}_{B}},\] at \[10{}^\circ C\] and \[2{}^\circ C\] respectively. If the water in both the vessels were compressed adiabatically and if we take into account the finite bulk modulus of elasticity of water, then \[{{T}_{A}}\] and \[{{T}_{B}}\]
Direction: An ideal diatomic gas is confined in a cylinder A of volume \[{{V}_{0}},\] this cylinder is connected to another cylinder B with the help of tube of a negligible volume. The cylinder B is fitted with a movable piston which can be adjusted from outside. Initially, the piston is adjusted so that volume of B is the same as volume of A i.e., \[{{V}_{0}}\]. B is evacuated and the stopcork is opened so that gas expands and occupies the volume \[2{{V}_{0}}\]. [System is thermally isolated from the surroundings].
During this free expansion, the internal energy of the system. Now with the stop-cork open, the piston is slowly moved to compress the gas back to cylinder A at temperature T. For this
Direction: An ideal diatomic gas is confined in a cylinder A of volume \[{{V}_{0}},\] this cylinder is connected to another cylinder B with the help of tube of a negligible volume. The cylinder B is fitted with a movable piston which can be adjusted from outside. Initially, the piston is adjusted so that volume of B is the same as volume of A i.e., \[{{V}_{0}}\]. B is evacuated and the stopcork is opened so that gas expands and occupies the volume \[2{{V}_{0}}\]. [System is thermally isolated from the surroundings].
Direction: An ideal diatomic gas is confined in a cylinder A of volume \[{{V}_{0}},\] this cylinder is connected to another cylinder B with the help of tube of a negligible volume. The cylinder B is fitted with a movable piston which can be adjusted from outside. Initially, the piston is adjusted so that volume of B is the same as volume of A i.e., \[{{V}_{0}}\]. B is evacuated and the stopcork is opened so that gas expands and occupies the volume \[2{{V}_{0}}\]. [System is thermally isolated from the surroundings].
In a cyclic process, a gas is taken from state A to B via path-I as shown in the indicator diagram and taken back to state A from state B via path-II. In the complete cycle:
A)
work is done by the gas
doneclear
B)
heat is ejected by the gas
doneclear
C)
no work is done by the gas
doneclear
D)
nothing can be said about work as data is insufficient
