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Heat is supplied to the gas, but its internal energy does not increase. What is the process involved?
From the first law of thermodynamics dQ = dU + dW, so clearly for the isothermal expansion or compression of a real gas where u = f(T) from the first law dU = 0 which means that the entire heat supplied is converted into work but from the second law of thermodynamics we find that in no process can the entire heat supplied can be converted into work hence in reality some fraction of heat supplied is always used to increase the internal energy of the system.
Extensive variable →H (enthalpy), E (Internal energy) and Mass. Since these variables depend on the amount of substance or volume or size of the system.
As work is a path function rather than a state function, we can easily say that work can often be graphically represented as the area under the PV graph. And as cyclic processes are represented as closed shapes on PV graph it is obvious that they have non zero area and thus work done is non zero.
From the first law of thermodynamics,
we know, dU = dQ  dW ; (work done BY the system is considered +ve)
For an adiabatic process, dQ = 0, and hence, dU = dW
For an ideal gas expansion, we see that work done
BY the system is +ve (recall the sign convention for work done), i.e., dW > 0.
Therefore, dU is less than 0, and thus, the internal energy decreases.
Find the final temperature of one mole of an ideal gas at an initial temperature to t K.The gas does 9 R joules of work adiabatically. The ratio of specific heats of this gas at constant pressure and at constant volume is 4/3.
T_{Initial } = t K
Work, W = 9R
Ratio of specific heats, γ = C_{p }/ C_{v} = 4/3
In an adiabatic process, we have
W = R(T_{Final }– T_{initial}) / (1γ)
9R = R (T_{Final }– t) / (1 – 4/3)
T_{Final} – t = 9 (1/3) = 3
T_{Final } = (t3) K
In an adiabatic process gas is reduced to quarter of its volume. What would happen to its pressure? Given ratio of specific heats γ= 2
Correct Answer : C
Explanation : The adiabatic condition is given by the relation between pressure volume and temperature volume as:
(PV)γ = constant
where, γ = Cp/Cv is ratio of the specific heats
These relations suggest that an decrease in volume is associated with increase in temperature
ATQ
P_{1}(V_{1})γ = (P_{2}V_{2})γ
=> P_{1}(1)^{2} = P_{2}(4)^{2}
P_{1}/P_{2} = 16
In an open system, for maximum work, the process must be entirely
A reversible process gives the maximum work.
Molar specific heat of a substance denoted by symbol C does not depend upon
The symbol c stands for specific heat and depends on the material and phase. The specific heat is the amount of heat necessary to change the temperature of 1.00 kg of mass by 1.00degreeC. The specific heat c is a property of the substance; its SI unit is J/(kg⋅K) or J/(kg⋅C).
Two gases X and Y kept in separate cylinders with same initial temperature and pressure are compressed to one third of their volume through isothermal and adiabatic process respectively. Which gas would have more pressure?
In which of the following processes is heat transfer equal to zero?
Entropy is defined as dQ/T. In an isentropic process dQ/T = 0 which means dQ = 0. Diathermic is a process in which heat flow is easily possible. Isochoric process is one in which volume is constant. Isothermal process is one in which temperature stays constant.
An isobaric expansion of a gas requires heat transfer to keep the pressure constant. An isochoric process is one in which the volume is held constant, meaning that the work done by the system will be zero.
Which of the following variables is zero for a cyclic process?
In a cyclic process, the starting position is the same as the ending position. So, the change in all state variables is zero. So the net change in internal energy is zero. ΔU = ΔQ – ΔW = 0.
Isothermal process can be represented by which law?
In an isothermal process, PV=const. This is the same as Boyle’s law. Charle’s law is given by: V/T=const. GayLussac’s law is given by: P/T=const and 2nd law of thermodynamics states that in every process total entropy of the universe must increase.
Calculate the work done by the gas in an isothermal process from A to B. P_{A} = 1Pa, V_{A} = 3m^{3}, P_{B} = 3Pa.
Since the process is isothermal the product PV will be constant.
P_{A}V_{A} = P_{B}V_{B}.
∴ V_{B} = 1*3/3 = 1m^{3}.
Work done in an isothermal process is given by:
nRT*ln(V_{B}/V_{A})
= P_{A}V_{A}ln(V_{B}/V_{A})
= 3 ln(1/3)
=  3.3 J.
In the given graph temperature remains constant with variation in volume. So the process is isothermal and PV = constant.
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