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Each molecule of a gas has f degrees of freedom. The radio $ { C_P \over C_V} = \gamma $ for the gas is
$C_p = \left( { f \over 2 } + 1 \right) R, C_v = {f \over 2} R $ $ { C_p \over C_v }= { \left( { f \over 2 } + 1 \right) R \over { f \over 2} R } = { {f \over 2} + 1 \over { f \over 2} } = { f+2 \over f} = 1 + { 2 \over f } $
If the ratio of specific heat of a gas at Consgant pressure to that at constant volume is $ \gamma $ , the Change in internal energy of the mass of gas, when the volume changes from V to 2V at Constant Pressure p, is
$ \triangle u = { P (V_2 - V_1) \over \gamma _1 } = { PV \over \gamma - 1 } $
The change in internal energy, when a gas is cooled from $ 927 ^\circ to 27 ^\circ C $
$ U \alpha T { u_1 \over u_2} = { T_1 \over T_2} $ $ \therefore { u_1 - u_2 \over u_2} = {T_1 - T_2 \over T_2} $
For hydrogen gas Cp - Cv = a and for oxygen gas Cp - Cv = b, The relation between a and b is given by
For all gases $ C_p - C_v = R $
In a thermodynamic process, pressure ofa fixed mass ofa gas is changed in such a manner that the gas release 20J of heat and 8J of work has done on the gas- If the inifial internal energy of the gas was 30j, then the final internal energy will be
$ \triangle Q = \triangle u + \triangle w $
If for a gas $ { Cp \over Cv } = 1.67 $ this gas is made up to molecules which are
$ { C_p \over C_v }= 1+ { 2 \over f} $
One mole of a monoatomic gas $ ( \gamma = 5 /3 ) $ is mixed with one mole ofA diatomic gas $ ( \gamma= 7/5 ) $ what will be value of $ \gamma $ for mixture ?
monoatomic gas cv = 3/2 R, diatomic gas cv = 5 /2 R, one mole of each gas is mixed $ C_v (mix) = {1 \over 2} \left[ { 3\over 2} R + { 5 \over 2} R \right] = 2R $ $C_p (mix) = R+ C_v $ =R + 2R = 3R $ r = { C_p mix \over C_v mix} = { 3R \over 2R } = 1.5 $
If du represents the increase in internal energy of a thesmodynamic system and dw the work done by the system, which of the following statement is true ?
dQ = du + dw
One mole of a monoatomic ideal gas is mixed with one mole of a diatomic ideal gas The molas specific heat of the micture at constant volume is ..........
$ C_v mix = { n_1 Cv_1 + n_2 Cv_2 \over n_1 + n_2 } $
One mole of a monoatomic gas is heate at a constant pressure of 1 atmosphere from 0k to 100 k. If the gas constant R = 8.32 J/mol k the change in internal energy of the gas is approximate ?
$ \triangle U = \gamma C_v \triangle T $
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