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I am answering this question:

Steam enters the superheaters of a boiler at a pressure of 25 bar and dryness of 0.98% and leaves at the same pressure at a temperature of 370 °C. Calculate the heat energy supplied by the superheaters.

The answer is supposed to be 405.51 J.

The Properties of Steam are:

At 25 bar and 370 °C: $h=3171.8\ \mathrm{kJ/kg}$

$h_{f}=962.11\ \mathrm{kJ/kg}$, $h_{fg}=1841.01\ \mathrm{kJ/kg}$

$h=h_f+xh_{fg}$

$h=962.11+0.98*1841.01=4070.474\ \mathrm{kJ/kg}$

$Q=m(h_2-h_1)=4070.474-3171.8=898.674$

What am I doing wrong?

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You just got the math wrong

$$h_1 = 962.11 + (0.98*1841.01) = 2766.2998 \ \mathrm{kJ/kg}$$ $$q = (h_2-h_1) = 3171.8 - 2766.2998 = 405.5 \ \mathrm{kJ/kg}$$

(I omitted your $m$ in final equation since we are calculating per kg.)

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