ΔU=q-w
= 100 - 50 = 50J
Since work is done by the system, it is -ve.

No transfer of heat or work is observed in an isolated system.
∴ΔU=q+w
ΔU=0+0=0.

If two systems at different temperatures are separately in thermal equilibrium with a third one, then they tend to be in thermal equilibrium with themselves.

First law of Thermodynamics.

T =298 K
ΔH 400 J mol^-1 = 400 J mol^-1
ΔS= 0.2 J K^-1 mol^-1
ΔG =ΔH-TΔS
if T =2000 K
ΔG = 400 - (0.2 \(\times\) 2000) = 0
if T > 2000 K
ΔG will be negative.
The reaction would be spontaneous only beyond 2000K.

\(\Delta { H }_{ f }^{ 0 }\)(SO₂) = - 297 kJ mol^-1
\(\Delta { H }_{ f }^{ 0 }\)(SO₃) = - 396 kJ mol^-1
SO₂ + \(\frac{1}{2}\)O₂⟶SO₃ \(\Delta { H }_{ r}^{ 0 }\)=?
\(\Delta { H }_{ r}^{ 0 }\)=\((\Delta { H }_{ f }^{ 0 })\)_compound-Σ(ΔH_f)_elements
\(\Delta { H }_{ r}^{ 0 }\)=​​​​\(\Delta { H }_{ f }^{ 0 }\)(SO₃)-(\(\Delta { H }_{ f }^{ 0 }\)(SO₂) +\(\frac{1}{2}\)\((\Delta { H }_{ f }^{ 0 })\)(O₂))
\(\Delta { H }_{ r}^{ 0 }\)=- 396 kJ mol^-1 - (-297 kJ mol^-1 + 0)
\(\Delta { H }_{ r}^{ 0 }\)=-396 kJ mol^-1 + 297
\(\Delta { H }_{ r}^{ 0 }\)=-99 kJ mol^-1

T= 33K
N₂O₄ \(\rightleftharpoons \) 2NO₂
Initial concentration 100% 
Concentration dissociated 50% 
Concentration remaining at equilibrium 50% 100%
K_eq=\(\frac{100}{50}=2\)
ΔG^o=-2.303 RT log Keq
ΔG^o=-2.303 x 8.314 x 33 x log 2
ΔG^o=-190.18 J mol^-1

n = 1mole
P = 4.1 atm
V= 2 L
T=?
q=3710 J
ΔS=\(\frac{q}{T}\)
ΔS=\(\frac { q }{ \left( \frac { PV }{ nR } \right) } \)
ΔS=\(\frac{nRq}{PV}\)
ΔS=\(\frac { 1\times 0.082\quad lit\quad atm{ K }^{ -1 }\times 3710J }{ 4.1\quad atm\times 2\quad lit } \)
ΔS​​​​​​​=37.10JK^-1

(i) Kelvin-Planck statement: It is impossible to construct a machine that absorbs heat from a hot source and converts it completely into work by a cyclic process without transferring a part of heat to a cold sink.
(ii) Clausius statement: It is impossible to transfer heat from a cold reservoir to a hot reservoir without doing some work.
(iii) Entropy statement: The entropy of an isolated system increases during a spontaneous process

Work is defined as the force (F) multiplied by the displacement(x).
-w = F.x.