Is heat and work are mutually convertible according to first law of thermodynamics?

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yes, they are. The only thing is that work is called high grade energy because almost all of it can be converted into heat. Whereas, heat is called low grade energy because never all of it gets converted into work. (This is nothing but 2nd law of thermodynamics.)
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GATE CRASHER

yes ,according to 1st law it is mutually convertible because it is a quantitaive law. it does not bother about the feasibility of the process.
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yes they are convertible take for example an ic engine,the power or heat energy generated by combustion of fuel.runs the crank which rotates and gets converted to mechanical work.
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A software engineer with more that 12 years of experience and 5 years of teaching experience

Yes the first law expresses the general law of conservation of energy. and states that heat and work are mutually convertible Heat In = Work Out over complete cycle or Sum (d Q ) = sum (d W ) Over a complete cycle the algebraic sum of the quantities of heat supplied to a system is equal to the...
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Yes the first law expresses the general law of conservation of energy. and states that heat and work are mutually convertible Heat In = Work Out over complete cycle or Sum (d Q ) = sum (d W ) Over a complete cycle the algebraic sum of the quantities of heat supplied to a system is equal to the algebraic sum quantities of work performed by the system i.e. In a cyclic process any property of the system are the same at the end of a cycle as at the beginning. Throughout the path of a cycle (?Q - ?W) represents a change in the total stored internal energy property of the system ?E . The basic energy equation results from this ?Q = ?E + ?W The total stored internal energy E includes for various forms of energy including the various forms of potential energy (gravity, magnetic, electrical) thermal energy chemical energy atomic energy kinetic energy surface tension energy Note: In classical thermodynamics as applicable to mechanical engineering the atomic energy and the chemical energy are not considered.... E = U + P.E + K.E + S.E P.E = total potential energy, K.E = total kinetic energy, S.E = total surface energy . The intrinsic internal energy U is the total internal energy minus the energies of motion, gravitational, magnetic and surface forces energies . The first law can be written using U as ?Q = ?U + ?W read less
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Mechanical Expert

Yes according to the first law of thermodynamics heat is convertable to work. Take the example of IC engine the heat energy is converted into mechanical work in the engine cylinder.
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