Question

How much steam at 100°C must be added to 163g of water at 250C contained in a 30 g glass vessel to produce water at 77°C?

Answer 1

Find the heat required:

$$m(r+c_w(t_s-t_f))=(m_wc_w+m_gc_g)(t_f-t_w),\\\space\\ m=\frac{(m_wc_w+m_gc_g)(t_f-t_w)}{r+c_w(t_s-t_f)}=0.016\text{ kg}.$$