Specific Heats MCQ Quiz in தமிழ் - Objective Question with Answer for Specific Heats - இலவச PDF ஐப் பதிவிறக்கவும்

Explanation:

For an ideal gas, the relationship between the specific heat capacities at constant pressure (Cp) and constant volume (Cv) is given by the equation:

Cp - Cv = R

where R is the universal gas constant. This equation indicates that Cp is always greater than Cv because R is a positive constant.

∴ Cp > Cv is the correct answer.

Concept:

• Heat required to raise the temperature of ice from -15°C to 0°C: Q₁ = m × c₁ × ΔT
• Heat required to melt ice at 0°C: Q₂ = m × L
• Heat required to raise the temperature of resulting water from 0°C to 10°C: Q₃ = m × c₂ × ΔT
• Total heat required: Q = Q₁ + Q₂ + Q₃

Calculation:

Mass of ice, m = 700 g = 0.7 kg

Initial temperature of ice, T₁ = -15°C

Final temperature of water, T₂ = 10°C

Specific heat of ice, c₁ = 2220 J/kg·K

Specific heat of water, c₂ = 4187 J/kg·K

Latent heat of fusion of ice, L = 333 kJ/kg

⇒ Heat to raise ice temperature:

Q₁ = 0.7 × 2220 × (0 - (-15))

⇒ Q₁ = 0.7 × 2220 × 15

⇒ Q₁ = 23.31 kJ

⇒ Heat to melt ice:

Q₂ = 0.7 × 333

⇒ Q₂ = 233.1 kJ

⇒ Heat to raise water temperature:

Q₃ = 0.7 × 4187 × (10 - 0)

⇒ Q₃ = 0.7 × 4187 × 10

⇒ Q₃ = 29.3 kJ

⇒ Total heat required:

Q = Q₁ + Q₂ + Q₃

⇒ Q = 23.31 + 233.1 + 29.3

⇒ Q ≈ 286 kJ

∴ The total heat required is approximately 286 kJ.

Concept:

Heat supplied at constant pressure = mC_p(T₂ - T₁)

Calculation:

Given:

m = 2 kg, T1 = 27°C, T2 = 127°C, C_p of oxygen = 0.918 kJ/kg-K (Experimental results)

Heat supplied at constant pressure = mCp(T2 - T1)

= 2 × 0.918 × (127 - 27) = 183.6 kJ

Explanation:

Heat Capacity (C):

It is the amount of energy or heat required to raise the temperature of a substance by 1 °C or 1 K.

It is the product of heat capacity (mc) and change in temperature (ΔT). It is given as -

Q = mcΔT = CΔT   ...... eq (1)

Q = heat required

C = mc = heat capacity of the substance (unit J/K or J/°C)

m = mass of the substance

c = heat capacity per unit mass

Specific heat (c):

It is the amount of energy or heat required to raise the temperature of the unit mass of a substance by 1 °C or 1 K. It is given by-

\(c =\frac{Q}{mΔ T}\)     eq.... (2)

Its unit is J/kg-K.

From eq(1) and (2)

C = mc ⇒ mass of substance × specific heat.

Concept:

• Perfect gas or ideal gas is the hypothatical condition which obeys the ideal gas law or the real nature of gas that is why its ideal condition.
• Specific heat is the quantity of heat required to raise the temperature of unit mass of the gas by 1 degree.
• Specific heat at constant pressure C_P is the quanity of heat required to raise 1 degree at constant pressure, and Specific heat C_V is the quantity of heat required to raise 1 degree at constant volume.

the specific heat is at constant pressure (Cp) is greater then the specific heat at constant volume (CV) And the gas constant can be expressed as CP - CV = R, this relation is termed as Mayer’s Formula.

Where,

R = Gas constant

n = molar mass of the substance

Cp= molar specific heat at constant pressure

CV = molar specific heat at constant Volume

Explanation:

We know that

\(\gamma = \frac{{{C_p}}}{{{C_v}}}\)

By rearranging the above equation we get,

\(\frac{{{C_p}}}{{{C_v}}} = \frac{1}{{\frac{{{C_p} - {C_p} + {C_v}}}{{{C_p}}}}}\)

∴ \(\frac{{{C_p}}}{{{C_v}}} = \frac{1}{{1 - \left( {\frac{{{C_p} - {C_v}}}{{{C_p}}}} \right)}}\)

∴ \(\gamma =\frac{{{C_p}}}{{{C_v}}} = \frac{1}{{1 - \left( {\frac{R}{{{C_p}}}} \right)}}\)

The specific heats of gases are generally expressed as molar specific heats. Two specific heats are defined for gases, one for constant volume (C_V) and one for constant pressure (C_P). These two specific heats are related by gas constant(R) as followed

Explanation:

Specific heat capacity:

• Specific heat capacity (s) of a substance is defined as the amount of heat (​ΔQ) per unit mass of the substance that is required to raise the temperature (ΔT) by 1°C.

s = \(\frac{1}{m} \frac{ΔQ}{ΔT}\)

• The unit of specific heat capacity is J/kg.K (J kg-1 K-1).

Explanation:

For polytropic process:

\({{W}_{12}}=\frac{{{P}_{1}}{{V}_{1}}-{{P}_{2}}{{V}_{2}}}{n-1}\)

\({{Q}_{12}}={{W}_{12}}+\text{ }\!\!\Delta\!\!\text{ }U=\frac{{{P}_{1}}{{V}_{1}}-{{P}_{2}}{{V}_{2}}}{n-1}+m{{c}_{v}}\left( {{T}_{2}}-{{T}_{1}} \right)=\frac{mR\left( {{T}_{1}}-{{T}_{2}} \right)}{n-1}+m{{c}_{v}}\left( {{T}_{2}}-{{T}_{1}} \right)\)

\({{Q}_{12}}=m\left( {{T}_{2}}-{{T}_{1}} \right)\left[ {{c}_{v}}-\frac{R}{n-1}~ \right]\)

\({{c}_{v}}-\frac{R}{n-1}={{c}_{v}}-\frac{{{c}_{p}}-{{c}_{v}}}{n-1}={{c}_{v}}-\frac{{{c}_{v}}\left( \gamma -1 \right)}{n-1}={{c}_{v}}\left[ 1-\frac{\left( \gamma -1 \right)}{n-1} \right]=\frac{{{c}_{v}}\left( n-\gamma \right)}{n-1}=\frac{{{c}_{v}}\left( \gamma -n \right)}{1-n}\)

\({{Q}_{12}}=m\left( {{T}_{2}}-{{T}_{1}} \right)\left[ {{c}_{v}}-\frac{R}{n-1}~ \right]=m\left( {{T}_{2}}-{{T}_{1}} \right)\frac{{{c}_{v}}\left( \gamma -n \right)}{1-n}\)

\({{Q}_{12}}=m\frac{{{c}_{v}}\left( \gamma -n \right)}{1-n}\left( {{T}_{2}}-{{T}_{1}} \right)=m{{c}_{n}}\left( {{T}_{2}}-{{T}_{1}} \right)\)

The polytropic specific heat of a gas is given by:

Heat lost by hot water = Heat gained by cold water + Heat gained by vessel

m_h C ΔT_h = m_c C ΔT_c + m_vc_v ΔT_v

40 × 4.2 × (60 – 30) = 50 × 4.2 × (30 – 20) + m_vc_v (30 – 20)

C_v = m_v c_v = 294 J/°C.