Question

Liq O2 at 50k is heated to 300k at const pressure 1 atm. Rate of heating is constant. Represent variation of temperature with time.?

Answer 1

Answer on Question #83879 - Physics - Molecular Physics| Thermodynamics

Liq O2 at 50k is heated to 300k at const pressure 1 atm. Rate of heating is constant. Represent variation of temperature with time.?

Solution. So, we have liquid oxygen at $50\mathrm{K}$ . We begin to heat it evenly at a pressure of 1 atmosphere. First, the heating will bring oxygen to the boiling point, let this point correspond to some temperature $\tau$ .

Consider a graph in the region from 50K to the boiling point of oxygen $\tau$ . The heat supplied to oxygen is calculated by the formula: $Q = cm\Delta T$ , where $c$ - liquid oxygen heat capacity; $m$ - mass of oxygen; $\Delta T$ - temperature change. For our considered area, the amount of heat supplied to oxygen will be written as: $Q = cm(\tau - 50)$ or the heat supplied during the time $t$ will be $\frac{Q}{t} = \frac{mc(\tau - 50)}{t}$ . In this case, the ratio $\frac{Q}{t} = const$ , because heat is supplied evenly. Then, $mc(\tau - 50) = const \times t$ . Then, addiction $T-t$ will be expressed as an inclined straight line with the ratio of the heat to the time on the dependency graph $T-t$ to a temperature $\tau$ from 50K.

Further, at the boiling point, heat will be expended to transfer oxygen from a liquid to a gaseous state, until all oxygen is converted to a gaseous state. In this case, the heat is expressed by the dependence: $Q_{1} = mL$ , where $L$ - latent heat of fluid transition to gas. Then the temperature dependence on time is expressed by a straight line parallel to the time axis.

When the evaporation process is complete, the temperature rises from the value of $\tau$ to value of 300K. In this interval, the amount of heat supplied to oxygen is written as: $Q_{2} = c_{g}m(300 - \tau)$ , where $c_{g}$ - heat capacity of gaseous oxygen. The dependence of temperature on time will be expressed by a straight line inclined to the time axis.

Thus, the graph of temperature versus time when heating oxygen from 50K to 300K will look like this:

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