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In a vessel, 10 kg of O2 is heated in a reversible now flow, constant volume process so that the pressure of O2 is increased two times of initial value. If the initial temperature is 20°C what will be the internal energy change (Cv = 0.65 kJ/kg k).
  • a)
    1904.5 kg
  • b)
    1804.5 kJ
  • c)
    1700 kJ
  • d)
    1600 kJ
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
In a vessel, 10 kg of O2 is heated in a reversible now flow, constant ...
m = 10 kg, P1 = P, P2 = 2p
T1 = 200 C
v = constant
T2 = 586 k
∆u = mc ∆T = 10 × 0.65 (586 − 293)
= 1904.5 kJ
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Most Upvoted Answer
In a vessel, 10 kg of O2 is heated in a reversible now flow, constant ...
Given data:
- Mass of O2 = 10 kg
- Initial pressure = P
- Final pressure = 2P
- Initial temperature = 20°C
- Specific heat at constant volume (Cv) = 0.65 kJ/kg K

Assumptions:
- The process is reversible, which means there is no heat transfer to the surroundings.
- The specific heat capacity remains constant throughout the process.

Calculating the change in internal energy:
The change in internal energy (ΔU) can be calculated using the first law of thermodynamics:

ΔU = Q - W

Where:
- ΔU is the change in internal energy
- Q is the heat transfer
- W is the work done

In this case, since the process is at constant volume, there is no work done (W = 0). Therefore, the change in internal energy simplifies to:

ΔU = Q

Calculating the heat transfer:
The heat transfer can be calculated using the equation:

Q = m * Cv * ΔT

Where:
- m is the mass of the substance (10 kg)
- Cv is the specific heat at constant volume (0.65 kJ/kg K)
- ΔT is the change in temperature

Calculating the change in temperature:
Since the process is isochoric (constant volume), the change in temperature can be calculated using the ideal gas law:

P1/T1 = P2/T2

Where:
- P1 is the initial pressure
- T1 is the initial temperature
- P2 is the final pressure
- T2 is the final temperature

Rearranging the equation, we get:

T2 = (P2 * T1) / P1

Substituting the values:
- P1 = P (initial pressure)
- T1 = 20°C + 273.15 (initial temperature in Kelvin)
- P2 = 2P (final pressure)

Substituting the values in the equation, we get:

T2 = (2P * (20+273.15)) / P = 546.3 K

Calculating the heat transfer:
Now that we have the final temperature, we can calculate the heat transfer:

Q = m * Cv * ΔT = 10 * 0.65 * (546.3 - 293.15) = 1904.5 kJ

Therefore, the change in internal energy (ΔU) is 1904.5 kJ, which corresponds to option A.
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In a vessel, 10 kg of O2 is heated in a reversible now flow, constant volume process so that the pressure of O2 is increased two times of initial value. If the initial temperature is 20°C what will be the internal energy change (Cv = 0.65 kJ/kg k).a)1904.5 kgb)1804.5 kJc)1700 kJd)1600 kJCorrect answer is option 'A'. Can you explain this answer?
Question Description
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