${P_1} = 1bar,$, ${T_1} = 37 = 273 + 37 = 310K$, ${P_2} = 15bars$, ${T_3} = 2000K,$ ${C_v} = 0.717KJ/KgK$, $\gamma = 1.4$
$${p_1}{v_1} = mR{T_1}$$$$1 \times 10 \times {v_1} = 1 \times 287 \times 310$$$${v_1} = 0.8897{m^3}$$$${p_2} \times v_2^\gamma = {p_1} \times v_1^\gamma $$$$15 \times v_2^\gamma = 1 \times {0.8897^{1.4}}$$$${v_2} = 0.1286{m^3}$$$$\frac{{{p_1}{v_1}}}{{{T_1}}} = \frac{{{p_2}{v_2}}}{{{T_2}}}$$$$\frac{{1 \times 0.8897}}{{310}} = \frac{{15 \times 0.1286}}{{{T_2}}}$$$${T_2} = 672.12K$$$$\frac{{{P_2}}}{{{T_2}}} = \frac{{{P_3}}}{{{T_3}}}$$$${P_3} = \frac{{15}}{{672.12}}2000 = 44.63bar$$$${p_4}v_4^\gamma = {p_3}v_3^\gamma $$$${p_4} = \frac{{44.63 \times {{0.1286}^\gamma }}}{{{{0.8897}^\gamma }}}$$$${p_4} = 2.976bar$$$${T_4} = \frac{{{p_4}}}{{{p_1}}}{T_1} = \frac{{2.97}}{1}310 = 920.7K$$$${Q_s} = {C_v}({T_3} - {T_2}) = 0.717(2000 - 672.12)$$$${Q_s} = 952.1Kj/kg$$$${Q_r} = {C_v}({T_4} - {T_1}) = 0.717(920.7 - 310) = 437.872K$$$$Work{\text{ done = 952}}{\text{.1 - 437}}{\text{.872 = 514}}{\text{.228Kj/Kg}}$$$$\eta = \frac{{Work{\text{ done}}}}{{heat{\text{ supply}}}} = \frac{{514.228}}{{952.1}}$$$$\eta = 0.5400 = 54\% $$