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Combined Gas Law Tutorial

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Combined Gas Law Tutorial

Combined Gas Law:
Combined Gas Law is a gas law which combines Charles's law, Boyle's law, and Gay-Lussac's law.

Combined Gas Law Formula :
Gas Equations: P_iV_i/T_i = P_fV_f/T_f
Initial Volume(V_i) = P_fV_fT_i / T_fP_i
Initial Pressure(P_i) = P_fV_fT_i / T_fV_i
Initial Temperature(T_i) = P_iV_iT_f / P_fV_f
Final Volume(V_f) = P_iV_iT_f / T_iP_f
Final Pressure(P_f) = P_iV_iT_f / T_iV_f
Final Temperature(T_f) = P_fV_fT_i / P_iV_i
where,
V_i = Initial Volume,
P_i = Initial Pressure,
T_i = Initial Temperature,
V_f = Final Volume,
P_f = Final Pressure,
T_f = Final Temperature.

Combined Gas Law Example:
Case 1: A cylinder contain a gas of volume 30 L, at a pressure of 110 kPa and a temperature of 420 K. Find the temperature of the gas which has a volume 40 L at a pressure of 120 kPa.
V_i = 30 L, P_i = 110 kPa, T_i = 420 K, V_f = 40 L, P_f = 120 kPa
Step 1: Substitute the values in the below final temperature equation:
Final Temperature(T_f) = P_fV_fT_i / P_iV_i
= (120 x 40 x 420) / (110 x 30)
= 2016000 / 3300
Final Temperature(T_f) = 610.91 K
This example will guide you to calculate the final temperature manually.

Case 2: A cylinder contain a gas of volume 10 L, at a pressure of 80 kPa and a temperature of 200 K. Find the temperature of the gas which has a volume 20 L at a temperature of 220 K.
V_i = 10 L, P_i = 80 kPa, T_i = 200 K, V_f = 20 L, T_f = 220 kPa
Step 1: Substitute the values in the below pressure equation:
Final Pressure(P_f) = P_iV_iT_f / T_iV_f
= (80 x 10 x 220) / (200 x 20)
= 176000 / 4000
Final Pressure(V_f) = 44 kPa
This example will guide you to calculate the pressure manually.

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