Change in P.E. = Heat energy

mgh = mS$$\Delta$$T

$$\Delta$$T = $${{gh} \over S}$$

= $${{10 \times 63} \over {4200J/kgC}}$$

= 0.147$$^\circ$$C

$${V_{rms}} = \sqrt {{{3KT} \over M}} $$

$${{{{({V_{rms}})}_{{O_2}}}} \over {{{({V_{rms}})}_{{H_2}}}}} = \sqrt {{{{M_{{H_2}}}} \over {{M_{{O_2}}}}}} = \sqrt {{2 \over {32}}} $$

$${({V_{rms}})_{{H_2}}} = 4 \times {({V_{rms}})_{{O_2}}}$$

$$ = 4 \times 160$$

$$ = 640$$ m/s

PT³ = constant

$$\left( {{{nRT} \over v}} \right)$$T³ = constant

T⁴ V^$$-$$1 = constant

T⁴ = kV

$$ \Rightarrow 4{{\Delta T} \over T} = {{\Delta V} \over V}$$ ....... (1)

$$\Delta$$V = V$$\gamma$$$$\Delta$$T ........ (2)

comparing (1) and (2), we get

$$\gamma = {4 \over T}$$

P_m = $$\rho$$RT

$$\therefore$$ $${{{P_1}} \over {{P_2}}} = {{{\rho _1}{T_1}} \over {{\rho _1}{T_2}}}$$

$${{{\rho _1}} \over {{\rho _2}}} \Rightarrow {{{P_1}{T_2}} \over {{P_2}{T_1}}} = \left( {{{76} \over {45}}} \right) \times {{266} \over {300}}$$

$${{{\rho _1}} \over {{\rho _2}}} \Rightarrow {{{M_1}} \over {{M_2}}} = {{76 \times 266} \over {45 \times 300}}$$

$$\therefore$$ $${M_2} \Rightarrow {{45 \times 300 \times 185} \over {76 \times 266}} = 123.54$$ kg