Question

Text: Specific heats (constant pressure and constant volume specific heats) of an ideal gas vary linearly with temperature as given: c(p) = a + kT and c(v) = b + kT Within the scope of the equations given above, the ideal gas is heated from temperature T1 to temperature T2. (a) Obtain an equation in terms of the change of specific entropy within the framework of variable specific heats. [using a, b, k, T1, T2, v1, v2] [v1 and v2 are the specific volumes of case 1 and case 2] (b) Obtain an equation regarding the change of specific entropy within the framework of variable specific heats in terms of [a, b, k, T1, T2, v1, v2, P1, P2] [P1 and P2 are the pressures of state 1 and state 2]. (c) Given: a = 15.573 kJ/kgK, b = 11.6129 kJ/kgK, k = 1.457*10^-3, P1/P2 = 0.324. Calculate the specific entropy change for T1 = 300 K and T2 = 1000 K within the framework of variable specific heats. Express the result in kJ/kgK. (d) Determine the v1/v2 ratio. 

          Text: Specific heats (constant pressure and constant volume specific heats) of an ideal gas vary linearly with temperature as given:
c(p) = a + kT and c(v) = b + kT
Within the scope of the equations given above, the ideal gas is heated from temperature T1 to temperature T2.
(a) Obtain an equation in terms of the change of specific entropy within the framework of variable specific heats. [using a, b, k, T1, T2, v1, v2] [v1 and v2 are the specific volumes of case 1 and case 2]
(b) Obtain an equation regarding the change of specific entropy within the framework of variable specific heats in terms of [a, b, k, T1, T2, v1, v2, P1, P2] [P1 and P2 are the pressures of state 1 and state 2].
(c) Given: a = 15.573 kJ/kgK, b = 11.6129 kJ/kgK, k = 1.457*10^-3, P1/P2 = 0.324. Calculate the specific entropy change for T1 = 300 K and T2 = 1000 K within the framework of variable specific heats. Express the result in kJ/kgK.
(d) Determine the v1/v2 ratio.
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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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Text: Specific heats (constant pressure and constant volume specific heats) of an ideal gas vary linearly with temperature as given: c(p) = a + kT and c(v) = b + kT Within the scope of the equations given above, the ideal gas is heated from temperature T1 to temperature T2. (a) Obtain an equation in terms of the change of specific entropy within the framework of variable specific heats. [using a, b, k, T1, T2, v1, v2] [v1 and v2 are the specific volumes of case 1 and case 2] (b) Obtain an equation regarding the change of specific entropy within the framework of variable specific heats in terms of [a, b, k, T1, T2, v1, v2, P1, P2] [P1 and P2 are the pressures of state 1 and state 2]. (c) Given: a = 15.573 kJ/kgK, b = 11.6129 kJ/kgK, k = 1.457*10^-3, P1/P2 = 0.324. Calculate the specific entropy change for T1 = 300 K and T2 = 1000 K within the framework of variable specific heats. Express the result in kJ/kgK. (d) Determine the v1/v2 ratio.
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Transcript

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00:01 From here in this question, we can say that the specific heats are the constant pressure and constant volume specific heats of an object which varies linearly with the temperature.
00:14 So, cp will be close to a plus kt and cv will be close to b plus kt...
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