JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II THERMODYNAMICS Previous Question Paper (March - 2022 - R13)
Answer any five questions. All questions carry equal marks.
Main
Differentiate between point function and path function and give examples for each of the functions.
Answer
A point function is a property of a system that depends only on the initial and final states of the system, and not on the path taken to get from one state to another. Its value is fixed for a given state.
A path function is a quantity that depends on the process or path followed by the system in going from one state to another. Its value is not fixed for a given state, but rather for a given process.
Examples:
Point Functions:
- Internal Energy (U)
- Enthalpy (H)
- Entropy (S)
- Temperature (T)
- Pressure (P)
- Volume (V)
Path Functions:
- Work (W)
- Heat (Q)
For instance, the work done by a gas during expansion depends on how the expansion occurs (e.g., isobarically, isothermally, adiabatically). Similarly, heat transfer depends on the process.
The internal energy and other thermodynamic properties of a certain fluid are given by
Answer
Given the internal energy relation: u = 211 + 0.191 T
And the ideal gas law: Pv = 0.287 (T+273)
Where: u is specific internal energy (kJ/kg), T is in degree C, P is pressure (kN/m²), and v is specific volume (m³/kg).
1. Specific heat at constant volume (c_v):
The fundamental relation for specific heat at constant volume is the partial derivative of internal energy with respect to temperature at constant volume:
From the given equation for internal energy, u = 211 + 0.191 T, we can differentiate it with respect to T. Since the equation for u is already given as a function of T only, and it does not explicitly depend on v, we can treat it as a direct derivative:
2. Specific heat at constant pressure (c_p):
The fundamental relation for specific heat at constant pressure involves enthalpy, but we can derive it using the first law of thermodynamics and the ideal gas law.
First, let's find the enthalpy (h). The relation is h = u + Pv.
Substitute the given relations:
Now, differentiate h with respect to T at constant P to find c_p:
Let's expand the enthalpy equation:
Now, differentiate h with respect to T:
Alternatively, using Mayer's relation for an ideal gas: c_p - c_v = R
From the ideal gas law Pv = RT', where T' is in Kelvin. Let's convert the given equation to use absolute temperature (T_K = T_C + 273).
This implies the gas constant R = 0.287 kJ/kg·K.
Using Mayer's relation:
Conclusion:
The specific heat at constant volume is c_v = 0.191 kJ/kg°C.
The specific heat at constant pressure is c_p = 0.478 kJ/kg°C.
What are the corollaries associated with the first law of thermodynamics? Explain the significance.
Answer
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0.25 m3 of air at 4 bar and 1000C is contained in a system. A reversible adiabatic expansion takes place till the pressure falls to 1.0 bar. The gas is then heated at constant pressure till enthalpy increases by 85 kJ. Calculate the work done and the index of expansion, if the above processes are replaced by a single reversible polytropic process giving the same work between the same initial and final states.
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State and explain the first law of thermodynamics and discuss its limitations.
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Two reversible heat engines A and B are arranged in series. Engine A rejects heat directly to engine B. A receives 200 kJ at a temperature of 4210C from the hot source while engine B is in communication with a cold sink at a temperature of 50C. If the work output of A is twice that of B, find: (i) intermediate temperature between A and B and (ii) efficiency of each engine.
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What do you understand by the term thermodynamic potential and discuss its significance?
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Steam at 1000 kPa, 2750C, enters a steady flow system with negligible velocity and leaves at 100 kPa, 1200C, with a velocity of 160 m/s. The flow rate is 9500 kg/hr. Heat is exchanged only with the surrounding atmosphere at 50C. Determine the maximum possible power output and irreversibility.
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Explain the process of throttling and free expansion and discuss their importance along with applications.
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One kg of steam initially at 1.01 MPa expands in a cylinder by following the law of expansion
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How to estimate the enthalpy, entropy and internal energy of gaseous mixtures? Give those equations.
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Determine the pressure exerted by CO2 using the Vander Waal’s equation. Take the constant values for a = 362850 Nm4/kg-mol2 and b = 0.0422 m2 kg-mol.
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What is the significance of adiabatic saturation? Explain how does it impact the air conditioning processes.
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Compare Otto, diesel and dual cycles for same compression ratio and for constant maximum pressure.
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A four cylinder petrol engine has a total swept volume of 2000 cm3 and the clearance volume in each cylinder is 60 cm3. If the pressure and temperature at the beginning of the compression are 1.02 bar and 240C, maximum cycle temperature is 14000C, Calculate: i) air standard efficiency ii) mean effective pressure.
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Draw P-V and T-s diagrams for Bell Coleman cycle of refrigeration and explain the salient features.
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