Thermodynamics - Common Formulae and Sample Problems -1
Temperature Conversion;
1. What is the equivalent temperature of 72°𝐹 to °𝐶? to °𝐾?
5 9
°𝐶 = 9
°𝐹 − 32 °𝐹 = 5
°𝐶 + 32 °𝐶 = °𝐾 − 273. 15
Thermal expansion;
2. A steel railroad track has a length of 30 mtrs when the temperature is 0°C. What is its length
on a hot day when the temperature is 40.0°C?
ɑ - coefficient of linear expansion, with unit of (°C)-1
∆L = ɑL o∆T Lf - Lo= ɑLo(Tf - To) Lf = ɑLo(Tf - To) + Lo
3. A steel ring with a hole having area of 3.99 cm 2 is to be placed on an aluminum rod with cross
sectional area of 4 cm2. Both rod and ring are initially at a temperature of 35 °C. At what
common temperature can the steel ring be slipped onto one end of the aluminum rod?
γ - coefficient of area expansion, with unit of (°C)-1 γ = 2ɑ
∆A = ɑA o∆T Af - A o= ɑAo(Tf - To) Af = ɑAo(Tf - To) + A o
, 4. A 1ltr aluminum cylinder at 5.00°C is filled to the brim with gasoline at the same temperature.
If the aluminum and gasoline are warmed to 65 °C, how much of the gasoline spills out?
β - coefficient of volume expansion, with unit of (°C)-1 β = 3ɑ
∆V = βVo∆T Vf - Vo= βVo(Tf - To) Vf = βVo(Tf - To) + Vo
Moles (Avogadro's number (Na) = 6.02 x10^23 particles/mole)
𝑚
𝑛 = 𝑚𝑜𝑙𝑎𝑟 𝑚𝑎𝑠𝑠 grms/mole
Ideal Gas;
Chemistry related formula;
Moles (Avogadro's number (Na) = 6.02 x1023 particles/mole)
𝑚
𝑛 = 𝑚𝑜𝑙𝑎𝑟 𝑚𝑎𝑠𝑠 grms/mole
A carbon atom has an atomic mass of 12 u, one atomic mass unit is equal to 1.66 x 10 -24 grms,
−24
1.66 𝑥 10 𝑔𝑟𝑚𝑠
𝑚𝑔𝑟𝑚𝑠 = 𝑁𝑎𝑚𝑎𝑡𝑜𝑚𝑖𝑐 (6.02 x10 ) (12 u) (
23
1𝑢
) = 12 grams/mole
The atomic mass units (u) of each element can be found in the periodic table.
5. An ideal gas at 20 °C and a pressure of 1.50 x 10 5 Pa is in a container having a volume of
1 ltr. Determine the number of moles of gas in the container.
PV = nRT (R is universal gas constant R = 8.31 J/mol.K)
6. An ideal gas at 20 °C and a pressure of 1.50 x 10 5 Pa is in a container having a volume of
1 ltr. The gas pushes against a piston, expanding to twice its original volume, while the pressure
falls to atmospheric pressure. What is the final temperature?
𝑃𝑓𝑉𝑓 𝑛𝑅𝑇𝑓 𝑃𝑓𝑉𝑓 𝑇𝑓
𝑃𝑖𝑉𝑖
= 𝑛𝑅𝑇𝑖 𝑃𝑖𝑉𝑖
= 𝑇𝑖
Temperature Conversion;
1. What is the equivalent temperature of 72°𝐹 to °𝐶? to °𝐾?
5 9
°𝐶 = 9
°𝐹 − 32 °𝐹 = 5
°𝐶 + 32 °𝐶 = °𝐾 − 273. 15
Thermal expansion;
2. A steel railroad track has a length of 30 mtrs when the temperature is 0°C. What is its length
on a hot day when the temperature is 40.0°C?
ɑ - coefficient of linear expansion, with unit of (°C)-1
∆L = ɑL o∆T Lf - Lo= ɑLo(Tf - To) Lf = ɑLo(Tf - To) + Lo
3. A steel ring with a hole having area of 3.99 cm 2 is to be placed on an aluminum rod with cross
sectional area of 4 cm2. Both rod and ring are initially at a temperature of 35 °C. At what
common temperature can the steel ring be slipped onto one end of the aluminum rod?
γ - coefficient of area expansion, with unit of (°C)-1 γ = 2ɑ
∆A = ɑA o∆T Af - A o= ɑAo(Tf - To) Af = ɑAo(Tf - To) + A o
, 4. A 1ltr aluminum cylinder at 5.00°C is filled to the brim with gasoline at the same temperature.
If the aluminum and gasoline are warmed to 65 °C, how much of the gasoline spills out?
β - coefficient of volume expansion, with unit of (°C)-1 β = 3ɑ
∆V = βVo∆T Vf - Vo= βVo(Tf - To) Vf = βVo(Tf - To) + Vo
Moles (Avogadro's number (Na) = 6.02 x10^23 particles/mole)
𝑚
𝑛 = 𝑚𝑜𝑙𝑎𝑟 𝑚𝑎𝑠𝑠 grms/mole
Ideal Gas;
Chemistry related formula;
Moles (Avogadro's number (Na) = 6.02 x1023 particles/mole)
𝑚
𝑛 = 𝑚𝑜𝑙𝑎𝑟 𝑚𝑎𝑠𝑠 grms/mole
A carbon atom has an atomic mass of 12 u, one atomic mass unit is equal to 1.66 x 10 -24 grms,
−24
1.66 𝑥 10 𝑔𝑟𝑚𝑠
𝑚𝑔𝑟𝑚𝑠 = 𝑁𝑎𝑚𝑎𝑡𝑜𝑚𝑖𝑐 (6.02 x10 ) (12 u) (
23
1𝑢
) = 12 grams/mole
The atomic mass units (u) of each element can be found in the periodic table.
5. An ideal gas at 20 °C and a pressure of 1.50 x 10 5 Pa is in a container having a volume of
1 ltr. Determine the number of moles of gas in the container.
PV = nRT (R is universal gas constant R = 8.31 J/mol.K)
6. An ideal gas at 20 °C and a pressure of 1.50 x 10 5 Pa is in a container having a volume of
1 ltr. The gas pushes against a piston, expanding to twice its original volume, while the pressure
falls to atmospheric pressure. What is the final temperature?
𝑃𝑓𝑉𝑓 𝑛𝑅𝑇𝑓 𝑃𝑓𝑉𝑓 𝑇𝑓
𝑃𝑖𝑉𝑖
= 𝑛𝑅𝑇𝑖 𝑃𝑖𝑉𝑖
= 𝑇𝑖
