A vessel contains helium, which expands at constant pressure when 15 kJ of heat is supplied to it. The work performed (in kJ) in the expansion will be ______.
- 6 KJ
- 12 KJ
- 4 KJ
- 9 KJ
The Correct Option is D
Solution and Explanation
Correct option is A)
The first law of thermodynamics gives us the relation:
q=ΔU+w
For constant pressure process,
q=nCpΔT
ΔU=nCvΔT
\(\frac{ΔU}{q}\)=CpCv=\(\frac{1}{γ}\)
Helium is a monoatomic gas i.e γ=\(\frac{5}{3}\)
ΔU=\(\frac{1}{γ}\)q=\(\frac{3}{5}\)×15kJ=9kJ
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(Given, atmospheric pressure = \(10^5 \, \text{N/m}^2\), density of mercury = \(1.36 \times 10^4 \, \text{kg/m}^3\), \(g = 10 \, \text{m/s}^2\), \(\pi = \frac{22}{7}\)) - In a container, 1 g of hydrogen and 1 g of oxygen are taken. Find the ratio of hydrogen pressure to oxygen pressure.
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Concepts Used:
Specific Heat Capacity
Specific heat of a solid or liquid is the amount of heat that raises the temperature of a unit mass of the solid through 1°C.
Molar Specific Heat:
The Molar specific heat of a solid or liquid of a material is the heat that you provide to raise the temperature of one mole of solid or liquid through 1K or 1°C.
Specific Heat at Constant Pressure or Volume:
The volume of solid remains constant when heated through a small range of temperature. This is known as specific heat at a constant volume. It is denoted as CV.
The pressure of solid remains constant when heated through a small range of temperature. This is known as specific heat at constant pressure which can be denoted as CP.