physics: pls!!!!! i need ur help.
in an experiment to verify Newton's law of cooling, the temperature of hot water in a calorimeter $T/^{o}C$ is plotted against time t/min. Which of the following is true about the graph? (a) The graph is linear and parallel to the T-axis. (b) the slope of the graph is positive. (c) the slope of the graph is negative. (d) the graph is hyperbola.
To determine which of the statements is true about the graph, let's first understand Newton's Law of Cooling. According to this law, the rate at which an object cools is directly proportional to the temperature difference between the object and its surroundings.
Now, let's analyze the given options:
(a) The graph is linear and parallel to the T-axis: This option is unlikely to be true since the law states that the rate of cooling is dependent on the temperature difference, meaning the graph should not be a straight line.
(b) The slope of the graph is positive: This option is not necessarily true. The slope of the graph could be positive or negative depending on the specific conditions of the experiment.
(c) The slope of the graph is negative: This option is a possibility. If the temperature is decreasing with time, the slope will indeed be negative.
(d) The graph is hyperbola: This option is unlikely to be true since a hyperbola is not typically associated with temperature vs. time relationships.
Based on the analysis, the correct answer is (c) the slope of the graph is negative. However, without additional information or data, it is not possible to definitively determine the exact shape or characteristics of the graph.
To determine which option is true about the graph, let's first understand what Newton's law of cooling is.
Newton's law of cooling states that the rate at which an object cools is proportional to the temperature difference between the object and its surroundings. Mathematically, it can be expressed as:
dT/dt = -k(T - Ts)
Where:
- dT/dt is the rate of change of temperature with respect to time,
- k is the cooling constant, and
- Ts is the temperature of the surroundings.
Now, let's analyze the options one by one:
(a) The graph is linear and parallel to the T-axis.
A linear graph parallel to the T-axis would represent no change in temperature with respect to time. This contradicts Newton's law of cooling, where temperature changes over time. Therefore, option (a) is not true.
(b) The slope of the graph is positive.
A positive slope indicates that the temperature is increasing with time. In the context of cooling, this would mean that the temperature is not decreasing, which is inconsistent with Newton's law of cooling. Therefore, option (b) is not true.
(c) The slope of the graph is negative.
A negative slope represents a decreasing temperature with respect to time. According to Newton's law of cooling, this is the expected behavior because the rate of cooling is proportional to the temperature difference between the object and its surroundings. Therefore, option (c) is true.
(d) The graph is a hyperbola.
A hyperbola graph would not represent the behavior of cooling over time. The equation of a hyperbola is not suitable for describing the relationship between temperature and time in the context of Newton's law of cooling. Hence, option (d) is not true.
In conclusion, the correct option is (c): the slope of the graph is negative.