S.No. |
Change or name of the process | Isobaric | Isochromic | Isothermal | Adiabatic |
1. |
Definition | P = Constant | V = Constant | T = Constant | a) Q = Constant
b) Entropy S = Constant |
2. | dQ | 1. For solids
dQ = mc_{p}dT For gases nc_{v}Dt 2. For change in state dQ = mL |
1. For solids
dQ = mc_{v}dT For gases nc_{v}dT |
dQ = dW |
Zero |
3. |
dU | 1. dQ-pdV
2. dQ-nRdT |
dQ | Zero | -dW |
4. | dW | 1. PdV
2. nRdT |
Zero | 2.303n Rt log v₂/v₁
2.303n p₁v₁ log v₂/v₁ 2.303n p₁v₁ log p₂/p₁ |
\[\frac{R\left( {{T}_{2}}-{{T}_{1}} \right)}{1-\gamma }\] \[\frac{\left( {{P}_{2}}{{V}_{2}}-{{P}_{1}}{{V}_{1}} \right)}{1-\gamma }\] |
5. |
Equation of state | V/T = Constant | P/T = Constant | PV = Constant
P₁V₁ = P₂V₂ |
PV^{γ}=constant
TV^{γ-1}=constant P^{1-γ }T^{γ}=constant |
6. |
Slope of p – v curve | Zero | ∞ | -p/v |
– γP/v |
7. | Law | Charle’s law | Gay-lussac’s law | Boyle’s law |
Poisson’s law |
8. |
Form of First laws | dQ = dU + dW = nc_{p}dT + PdV | dQ = dU = nc_{v}dT | dQ = dW = dV | – dU = dW |
9. | Bulk modulus | Zero | Infinity | -p |
-γp |
10. | Result of maximum work | Maximum | Zero | Less from isobaric process but greater form adiabatic process |
Minimum but not zero |
Example: A cylinder with a movable piston contains 3 moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase if the gas is compressed to half its original volume?
Ans: As no heat is allowed to be exchanged, the process is adiabatic.
As V₂ = V₁/2.