A constant mass of gas maintained at constant pressure has a volume of 2.5×10⁴ at 0°c and 3.15×10⁴ at 100°c and 6.52×10⁴ at normal boiling point of sulphur the temperature corresponding to the boiling point of sulphur is

Physics

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Answer

618∘C618^\circ C

Step-by-step solution

3 steps
  1. Understand the relationship between volume and temperature.

    For a constant mass of gas maintained at constant pressure, the volume (VV) is linearly related to the Celsius temperature (TCT_C). This relationship can be expressed as V=aTC+bV = aT_C + b, where aa and bb are constants.

  2. Use the given data points to find the constants aa and bb.

    We have two known points:

    1. At TC=0∘CT_C = 0^\circ C, V=2.5×104V = 2.5 \times 10^4.
    2. At TC=100∘CT_C = 100^\circ C, V=3.15×104V = 3.15 \times 10^4.

    Substitute the first point into the equation:

    2.5×104=a(0)+b2.5 \times 10^4 = a(0) + b b=2.5×104b = 2.5 \times 10^4

    Substitute the second point and the value of bb into the equation:

    3.15×104=a(100)+2.5×1043.15 \times 10^4 = a(100) + 2.5 \times 10^4 100a=3.15×104−2.5×104100a = 3.15 \times 10^4 - 2.5 \times 10^4 100a=(3.15−2.5)×104100a = (3.15 - 2.5) \times 10^4 100a=0.65×104100a = 0.65 \times 10^4 a=0.65×104100a = \frac{0.65 \times 10^4}{100} a=0.65×102a = 0.65 \times 10^2 a=65a = 65

    So, the relationship between volume and temperature is:

    V=65TC+2.5×104V = 65T_C + 2.5 \times 10^4
  3. Calculate the temperature corresponding to the boiling point of sulfur.

    We are given that the volume at the normal boiling point of sulfur is V=6.52×104V = 6.52 \times 10^4. Let this temperature be TST_S.
    Substitute this volume into the derived equation:

    6.52×104=65TS+2.5×1046.52 \times 10^4 = 65T_S + 2.5 \times 10^4 65TS=6.52×104−2.5×10465T_S = 6.52 \times 10^4 - 2.5 \times 10^4 65TS=(6.52−2.5)×10465T_S = (6.52 - 2.5) \times 10^4 65TS=4.02×10465T_S = 4.02 \times 10^4 TS=4.02×10465T_S = \frac{4.02 \times 10^4}{65} TS=4020065T_S = \frac{40200}{65} TS≈618.4615T_S \approx 618.4615

    Rounding to three significant figures, consistent with the input data:

    TS≈618∘CT_S \approx 618^\circ C

    The temperature corresponding to the boiling point of sulfur is 618∘C\boxed{618^\circ C}.

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