# Calculation of Work and Heat in Various Processes

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Energy in a thermodynamic System can be transferred in three ways namely Work, Heat and by mass. A closed System and its Surroundings can interact by work transfer and Heat transfer, whereas open system can interact by work, Heat and mass transfer (because mass also carries energy).

Energy in a thermodynamic System can be transferred in three ways namely Work, Heat and by mass. A closed System and its Surroundings can interact by work transfer and Heat transfer, whereas open system can interact by work, Heat and mass transfer (because mass also carries energy).

WORK TRANSFER
Work can be defined as force multiplied by distance moved by object in the direction of applied load; we call it as mechanical work.

“Work is said to be done by a system if the sole effect on things external to the system can be used to raising of a weight”.

Consider the Battery and motor as system. The motor is driving a fan. When the fan is replaced by pulley and weight, the weight can be raised by distance x. Thus, sole effect or ultimate effect external to system is raising of weight.

HEAT TRANSFER

Consider two body A & B having temperature TA & TB (TA >TB) respectively. When these two body came in contact with each other (or kept in the vicinity of each other) then there will be transfer of energy will takes place from high temperature body to low temperature body.

“The energy transfer because of the temperature difference is known as Heat”

Sometimes heat transfer takes place without the change in temperature but due to effect.

SIGN CONVENTION FOR WORK TRANSFER
Work done by system is taken as Positive and work done on system is negative.

Heat supplied to the system is taken as positive and heat rejected from the system is taken as negative.

GENERALIZED EQUATION FOR NON-FLOW WORK OR CLOSED SYSTEM WORK

If the Process is Quasi-static (the intermediate Position is also in equilibrium). For very small movement dx of Piston from this intermediate state
F = PA → acting on Piston.

δ W = F×dx
δ W = P dv

It we draw a graph between pressure and volume and consider a small part of this graph, the area of small element on volume axis is

PATH FUNCTION- Path function are inexact differential, so we use δϕ. Work and heat both are path function.

REVERSIBLE CONSTANT VOLUME OR ISOCHORIC PROCESS-

W = 0

dQ = mcvΔT

REVERSIBLE CONSTANT PRESSURE OR ISOBARIC PROCESS-

W = P (V2 – V1)

dQ = mcPΔT

REVERSIBLE ISOTHERMAL PROCESS-

dQ = dW

Q = 0

This topic is important for GATE MEISRO MEESE IES ME, and other Mechanical exams.

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