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One mole of an ideal gas whose adiabatic exponent equals R undergoes a process in which the gas pressure relates to the temperature as P = aTα. The work performed by the gas if its temperature gets an increment ΔT.
  • a)
    -R (1 - α )ΔT
  • b)
    -R (1 + α )ΔT
  • c)
    R (1 -α )ΔT
  • d)
    R (1 + α )ΔT
Correct answer is option 'C'. Can you explain this answer?
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One mole of an ideal gas whose adiabatic exponent equals R undergoes a...
p = aTα


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One mole of an ideal gas whose adiabatic exponent equals R undergoes a...
To solve this problem, let's start with the ideal gas law:

PV = nRT

where:
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant
T = temperature

Since we're given that the gas pressure relates to the temperature as P = aT, we can substitute this into the ideal gas law equation:

(aT)V = nRT

Next, let's consider the adiabatic exponent, γ. For an ideal gas, γ is defined as the ratio of specific heat capacities:

γ = Cp/Cv

where:
Cp = specific heat capacity at constant pressure
Cv = specific heat capacity at constant volume

Since the gas is an ideal gas, γ is constant. Given that the adiabatic exponent equals R, we have:

γ = R

Now, let's consider an adiabatic process, where no heat is exchanged with the surroundings. In an adiabatic process, the relationship between pressure and volume is given by:

PV^γ = constant

Substituting the equation relating pressure to temperature, we have:

(aT)V^γ = constant

Since we are given that there is one mole of gas, we can substitute n = 1 into the ideal gas law equation:

(aT)V = RT

Rearranging this equation, we have:

V = RT/aT

Simplifying, we find:

V = R/a

So, in an adiabatic process, the volume of one mole of gas is directly proportional to the ideal gas constant divided by the constant of proportionality, a.

Note: The adiabatic exponent being equal to R is not a typical scenario for an ideal gas. Usually, γ takes on values between 1 and 2, depending on the gas.
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One mole of an ideal gas whose adiabatic exponent equals R undergoes a...
p = aTα


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One mole of an ideal gas whose adiabatic exponent equals R undergoes a process in which the gas pressure relates to the temperature as P = aTα. The work performed by the gas if its temperature gets an increment ΔT.a)-R (1 - α )ΔTb)-R (1 + α )ΔTc)R (1 -α )ΔTd)R (1 + α )ΔTCorrect answer is option 'C'. Can you explain this answer?
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