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For a givenidealgas 6xx 10^(5) J heatenergyissuppliedand the volumeof gas isincreased from 4m^(3) to 6 m^(3) atatmosphericpressure .Calculate(a) theworkdoneby thegas( b) Changein internalenergyof thegas ( c)graphthisprocessinPV andTVdiagram

Answer» <html><body><p></p>Solution :Mayer.s relation: Consider u mole of an ideal gas in a <a href="https://interviewquestions.tuteehub.com/tag/container-20566" style="font-weight:bold;" target="_blank" title="Click to know more about CONTAINER">CONTAINER</a> with volume V, pressure P and temperature T. <br/> When the gas is heated at constant volume the temperature increases by dt. As no work is done by the gas, the heat that flows into the system will increase only the internal energy. Let the change in internal energy be dU. <br/> If `C_v` is the molar specific heat capacity at constant volume, from equation. <br/>` C_v= 1/mu( d U )/(dT )`<br/> `dU= mu C _vdT` <br/> Suppose the gas is heated at constant pressure so that the temperature increases by dT. If .Q. is the heat supplied in this <a href="https://interviewquestions.tuteehub.com/tag/process-11618" style="font-weight:bold;" target="_blank" title="Click to know more about PROCESS">PROCESS</a> and .dV. the change in volume of the gas.<br/>`Q=mu C _(p ) dT `...(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>) <br/> If W is the work done by the gas in this process, then <br/>`W= PDV` <br/> But from the first law of thermodynamics, <br/> `Q=dU + W `<br/> Substituting equations (2), (3) and (4) in (5), we get, <br/> `mu C _(p) dT= muC_(v)dT+ p dV `<br/>For mole of ideal gas, the equation of state is given by <br/>`PV = mu RTimplies <a href="https://interviewquestions.tuteehub.com/tag/pd-590584" style="font-weight:bold;" target="_blank" title="Click to know more about PD">PD</a> V +dp = mu R d T`<br/> Since the pressure is constant, dP = 0 <br/>`thereforeC_P dT= C_(v)dT+ RdT`<br/> ` thereforeC_(P)= C_(V)+R (or )C_(P ) - C_(V )= R ` <br/>This relation is called Mayer.s relation It <a href="https://interviewquestions.tuteehub.com/tag/implies-1037962" style="font-weight:bold;" target="_blank" title="Click to know more about IMPLIES">IMPLIES</a> that the molarspecificheatcapacity of an ideal gas at constant pressure is greater than molar specificheat capacityatconstantvolume <br/>therealationshowsthat specificheatatconstantpressure`(s_p)`is alwaysthancalculatethe workdoneby thegas <br/>(ii) A gas expands from volume `1m^3` to `2m^3` at constant atmospheric pressure.<br/>(ii )The pressure P = 1 atm = 101 kPa,<br/> ` V_f= 2 m^3 and V_i= 1 m^3`<br/>From equation ` W =int_(v_i)^(v_f) pdV = Pint _(vi)^(vi) dv `<br/>Since P is constant. It is taken o’t of the integral. <br/> `W=P (V_f -V_f ) = 10 1 xx 10^3xx ( 2-1)= 101 KJ`</body></html>


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