An ideal gas is taken through a cyclic thermodynamical process through four steps. The amounts of heat involved in these steps are Q1=5960 textJ, Q2=-5585 textJ, Q3=-2980 textJ and Q4=3645 textJ, respectively. The corresponding works involved are W1=2200 textJ, W2=-825 textJ, W3=-1100 textJ and W4, respectively. The value of W4 is

Question

An ideal gas is taken through a cyclic thermodynamical process through four steps. The amounts of heat involved in these steps are Q1=5960 textJ, Q2=-5585 textJ, Q3=-2980 textJ and Q4=3645 textJ, respectively. The corresponding works involved are W1=2200 textJ, W2=-825 textJ, W3=-1100 textJ and W4, respectively. The value of W4 is (A) 1315J (B) 275J (C) 765J (D) 675J

Tardigrade Admin · Accepted Answer

As, Δ Q=Q1+Q2+Q3+Q4 =5960-5585-2980+3645 =1040 textJ Also, Δ W=W1+W2+W3+W4 =2200-825-1100+W4 =275+W4 For a cyclic process, Δ U=0 i.e., Uf-Ui=0, From first law of thermodynamics Δ Q=Δ U+Δ W 1040=0+275+W4 Or W4=765 textJ

$1315 J$

$275 J$

$765 J$

$675 J$

1315J

275J

765J

675J

As, ΔQ=Q1​+Q2​+Q3​+Q4​ =5960−5585−2980+3645 =1040J Also, ΔW=W1​+W2​+W3​+W4​ =2200−825−1100+W4​ =275+W4​ For a cyclic process, ΔU=0 i.e., Uf​−Ui​=0, From first law of thermodynamics ΔQ=ΔU+ΔW 1040=0+275+W4​ Or W4​=765J

$1315 J$

$275 J$

$765 J$

$675 J$