1st Example: Combustion heater

A heater warms up water using butane, with a heating value of p_c=MJ/kg, and it has an efficiency of η=%, providing a flow rate of q=L/min while causing an increase in its temperature of Δt=℃. Butane is obtained from gas cylinders holding m_b=kg, which cost c_b=€. Water's specific heat is of c_p=J/(g K). Under these conditions, determine:

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• b)q_comb, fuel consumption in grams per second.
• c)c, cost in €, and m_comb mass of the fuel consumed during a time frame of t=min.

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Solutions

• a)\[P=\frac{E}{t}=\frac{Cp*m*Δt}{t}=Cp*q*ρ*Δt\] P=W
  Note:ρ represents water's density, which is ρ=1kg/L
• b) \[q_{comb}=\frac{m_{b}}{t_{b}}=\frac{m_{b}*P_{b}}{E_{b}}=\frac{m_{b}*P_{b}}{p_{c}*m_{b}}=\frac{P}{p_{c}*η}=\frac{Cp*q*ρ*Δt}{p_{c}*η}\] \[q_{comb}=\]g/s
  Note:ρ represents water's density, which is ρ=1kg/L
• c) \[c=\frac{m_{comb}*c_{b}}{m_{b}}→m_{comb}=?→m_{comb}=q_{comb}*t=\frac{Cp*q*ρ*Δt*t}{p_{c}*η}\] \[m_{comb}=\]kg
  \[c=\frac{m_{comb}*c_{b}}{m_{b}}\] \[c=\]€
  Note:ρ represents water's density, which is ρ=1kg/L