Thermodynamics

Inner energy of monatomic gas
$$U = \frac{3\cdot m\cdot R\cdot T}{2\cdot M}$$
U - inner energy of the gas
m - mass
R - ideal gas constant
T - temperature
M - molar mass
Find   It is known that:
      =   
Calculate 'U'

Inner energy of monatomic gas
$$U = \frac{3\cdot \nu\cdot R\cdot T}{2}$$
U - inner energy of the gas
ν - amount of substance
R - ideal gas constant
T - temperature
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      =   
Calculate 'U'

Specific heat of gas
$$c = \frac{3\cdot R}{2}\cdot M$$
c - specific heat
R - ideal gas constant
M - molar mass
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      =   
Calculate 'c'

Gas expansion work
$$A = p\cdot \Delta_{V}$$
A - work
p - pressure
Δ_V - change in volume
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      =   
Calculate 'A'

Work of isothermal expansion of the gas
$$A = \frac{m\cdot R\cdot T}{M}\cdot ln(\frac{V_{2}}{V_{1}})$$
A - work
m - mass
R - ideal gas constant
T - temperature
M - molar mass
V2 - final volume
V1 - initial volume
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      =   
Calculate 'A'

The first law of thermodynamics
$$\Delta_{U} = A+Q$$
Δ_U - internal energy change
A - work done by the system
Q - amount of heat transferred to the system
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      =   
Calculate 'Δ_U'

Efficiency of heat engine
$$\eta = \frac{A_{n}}{Q_{1}}$$
η - efficiency
A_n - efficient (useful ) job
Q_1 - received amount of heat
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      =   
Calculate 'η'

Efficiency of heat engine
$$\eta = \frac{Q_{1}-Q_{2}}{Q_{1}}$$
η - efficiency
Q_1 - received amount of heat
Q_2 - heat rejected to the cooler
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      =   
Calculate 'η'

Maximum efficiency of heat engine
$$\eta_{max} = \frac{T_{1}-T_{2}}{T_{1}}$$
η_max - maximum efficiency
T1 - heater temperature
T2 - coller temperature (cold reservoir)
Find   It is known that:
      =   
Calculate 'η_max'

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